# apu math302 full course [ all forums all quizes midterm and final ]

forumsweek 4

Suppose that a class contains 15 boys and 30 girls, and that

10 students are to be selected at random for a special assignment. Find the

probability that exactly 3 boys will be selected.

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week 6

Suppose that the percentage annual return you obtain when

you invest a dollar in gold or the stock market is dependent on the general

state of the national economy as indicated below. For example, the probability

that the economy will be in “boom” state is 0.15. In this case, if

you invest in the stock market your return is assumed to be 25%; on the other

hand if you invest in gold when the economy is in a “boom” state your

return will be minus 30%. Likewise for the other possible states of the economy.

Note that the sum of the probabilities has to be 1–and is.

State of economy Probability Market Return Gold Return

Boom 0.15 25% (-30%)

Moderate Growth 0.35 20% (-9%)

Week Growth 0.25 5% 35%

No Growth 0.25 (-14%) 50%

Based on the expected return, would you rather invest your

money in the stock market or in gold? Why?

Keep in mind that your post must be made by 11:55PM EASTERN

time on Wednesday during the week in which a discussion question is posed. I

will evaluate your responses to each of these questions using a 0 to 10 point

scale, and your contribution to each of the five Discussion Forums will count

as 2 percent of the overall course grade for a total of 10 percent.

My evaluation of your post will be based on the extent to

which you participated and fostered a positive and effective learning

environment–for yourself and others. Participating and sharing are the keys.

Naturally, simply copying someone else’s post is prohibited. Your post should

reflect your understanding of the question posed. In addition to the

computations you employed to arrive at your response, your post must contain

comments regarding the rationale for the approach you utilized. Simply listing

an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the

Decision Alternatives link, then click Start a New Conversation. In the title

block of the dialog box that appears insert your first and last name; compose

your post in the message box; and then click Post Message.

week 7

Suppose that the demand for a company’s product in weeks 1,

2, and 3 are each normally distributed and the mean demand during each of these

three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of

the demand during each of these three weeks is known to be 10, 5, and 15,

respectively. It turns out that if we can assume that these three demands are

probabilistically independent then the total demand for the three week period

is also normally distributed. And, the mean demand for the entire three week

period is the sum of the individual means. Likewise, the variance of the demand

for the entire three week period is the sum of the individual weekly variances.

But be careful! The standard deviation of the demand for the entire 3 week

period is not the sum of the individual standard deviations. Square roots don’t

work that way!

Now, suppose that the company currently has 180 units in

stock, and it will not be receiving any further shipments from its supplier for

at least 3 weeks. What is the probability that the company will run out of

units?

Keep in mind that your post must be made by 11:55PM EASTERN

time on Wednesday during the week in which a discussion question is posed. I

will evaluate your responses to each of these questions using a 0 to 10 point

scale, and your contribution to each of the five Discussion Forums will count

as 2 percent of the overall course grade for a total of 10 percent.

My evaluation of your post will be based on the extent to

which you participated and fostered a positive and effective learning

environment–for yourself and others. Participating and sharing are the keys.

Naturally, simply copying someone else’s post is prohibited. Your post should

reflect your understanding of the question posed. In addition to the

computations you employed to arrive at your response, your post must contain

comments regarding the rationale for the approach you utilized. Simply listing

an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the

Using the Normal Distribution link, then click Start a New Conversation. In the

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week 10

Political polls typically sample randomly from the U.S

population to investigate the percentage of voters who favor some candidate or

issue. The number of people polled is usually on the order of 1000. Suppose

that one such poll asks voters how they feel about the President’s handling of

the crisis in the financial markets. The results show that 575 out of the 1280

people polled say they either “approve” or “strongly approve” of the

President’s handling of this matter. Based on the sample referenced above, find

a 95% confidence interval estimate for the proportion of the entire voter

population who “approve” or “strongly approve” of the President’s handling of

the crisis in the financial markets.

Now, here’s an interesting twist. If the same sample

proportion was found in a sample twice as large—that is, 1150 out of 2560—how

would this affect the confidence interval?

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time on Wednesday during the week in which a discussion question is posed. I

will evaluate your responses to each of these questions using a 0 to 10 point

scale, and your contribution to each of the five Discussion Forums will count

as 2 percent of the overall course grade for a total of 10 percent.

which you participated and fostered a positive and effective learning

environment–for yourself and others. Participating and sharing are the keys.

Naturally, simply copying someone else’s post is prohibited. Your post should

reflect your understanding of the question posed. In addition to the

computations you employed to arrive at your response, your post must contain

comments regarding the rationale for the approach you utilized. Simply listing

an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the

Build a Confidence Interval Estimate link, then click Start a New Conversation.

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week 12

A new process for producing synthetic diamonds can be

operated at a profitable level only if the average weight of the diamonds

produced by the process is greater than 0.5 karat. To evaluate the

profitability of the process, a sample of six diamonds was generated using this

new process, with recorded weights .46, .61, .52, .48, .57, and .54 karat. Do

the six measurements present sufficient evidence to indicate that the average

weight of the diamonds produced by the new process is in excess of 0.5 karat? To

answer this question conduct an appropriate test of hypothesis using the five

step process outlined in our textbook and utilized in the solutions to the

Chapter 8 review problems, which can be accessed via the link in the

Assignments, Tests & Quizzes sub-section in the weekly lesson that can be

found in the Lessons section of our classroom.

Keep in mind that your post must be made by 11:55PM EASTERN

time on Wednesday during the week in which a discussion question is posed. I

will evaluate your responses to each of these questions using a 0 to 10 point

scale, and your contribution to each of the five Discussion Forums will count

as 2 percent of the overall course grade for a total of 10 percent.

which you participated and fostered a positive and effective learning

environment–for yourself and others. Participating and sharing are the keys.

Naturally, simply copying someone else’s post is prohibited. Your post should

reflect your understanding of the question posed. In addition to the

computations you employed to arrive at your response, your post must contain

comments regarding the rationale for the approach you utilized. Simply listing

an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the

Testing a Hypothesis link, then click Start a New Conversation. In the title

block of the dialog box that appears insert your first and last name; compose

your post in the message box; and then click Post Message.

quizesQuestion 1 of 201.0/ 1.0 PointsA variable is classified as ordinal if:A.we track the variable through a period of timeB.the data arise from continuous measurementsC.there is a natural ordering of categoriesD.there is no natural ordering of categoriesQuestion 2 of 201.0/ 1.0 PointsWhich of the following indicates how many observations fall into various categories?A.The sample tableB.The tabulation scaleC.The frequency tableD.The Likert scaleQuestion 3 of 201.0/ 1.0 PointsFind the z-score for each student and indicate which one has a better relative position. An Art Major earned a grade of 46 on an exam with f$ar{x}f$ = 50 and s = 5; A Theater Major earned a grade of 70 on an exam with f$ar{x}f$ = 75 and s = 7.A.The art major has a higher relative position than the theater major.B.Both students have the same score.C.The theater major has a higher relative position than the art major.D.The higher score cannot be determined.Question 4 of 201.0/ 1.0 PointsWhich of the following is the graphical analog of a frequency table?A.The scatterplotB.The time series plotC.The histogramD.The contingency tableQuestion 5 of 201.0/ 1.0 PointsWhich of the following are the three most common measures of central location?A.Mean, variance, and standard deviationB.Mean, median, and modeC.Mean, median, and varianceD.Mean, median, and standard deviationQuestion 6 of 201.0/ 1.0 PointsSuppose that a histogram of a data set is approximately symmetric and “bell shaped”. Approximately, what percent of the observations are within three standard deviations of the mean?A.95%B.99.7%C.50%D.68%Question 7 of 200.0/ 1.0 PointsWhat type of sampling is being employed if the population is divided into economic classes and a sample is chosen from each economic class to be surveyed?In A.cluster samplingB.systematic samplingC.stratified samplingD.random samplingQuestion 8 of 201.0/ 1.0 PointsThe length of the box in the boxplot portrays theA.interquartile rangeB.medianC.meanD.rangeQuestion 9 of 201.0/ 1.0 PointsWhat kind of relationship between x and y is demonstrated by the scatter plot below?A.A positive linear relationshipB.No linear relationshipC.This is not a scatter plotD.A negative linear relationshipQuestion 10 of 201.0/ 1.0 PointsA population includes:A.only householdsB.all objects of interest in a particular studyC.only machinesD.only peopleQuestion 11 of 201.0/ 1.0 PointsSuppose that a histogram of a data set is approximately symmetric and “bell shaped”. Approximately what percent of the observations are within one standard deviation of the mean?A.99.7%B.68%C.95%D.50%Question 12 of 201.0/ 1.0 PointsThe difference between the first and third quartile is called theA.mid rangeB.interquartile rangeC.unimodal rangeD.interdependent rangePart 2 of 3 – 2.0/ 6.0 PointsQuestion 13 of 200.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.The histogram below represents scores achieved by 250 job applicants on a personality profile.The histogram below represents scores achieved by 250 job applicants on a personality profile.Sixty percent of the job applicants scored below what value? Place your answer in the blank. Do not use any stray symbols. For example, 123 would be a legitimate answer..30Question 14 of 200.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.Compute the median number of children. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry. 1.90Question 15 of 200.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.Compute the variance of the data. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry. 2.49Question 16 of 201.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.Did Well on Exam Did Poorly on ExamStudying for Exam 60 15Went Partying 22 53If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitimate answer. 10.00Question 17 of 201.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.The histogram below represents scores achieved by 250 job applicants on a personality profile.The histogram below represents scores achieved by 250 job applicants on a personality profile.Seventy percent of the job applicants scored above what value? Place your answer in the blank. Do not use any stray symbols. For example, 123 would be a legitimate answer.20Question 18 of 200.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.Did Well on Exam Did Poorly on ExamStudying for Exam 60 15Went Partying 22 53If the sample is a good representation of the population, what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitmate answer. 20.00Part 3 of 3 – 1.0/ 2.0 PointsQuestion 19 of 200.0/ 1.0 PointsA histogram is skewed to the left (or negatively skewed) if it has a single peak and the values of the distribution extend much further to the right of the peak than to the left of the peak.InTrueFalseAnswer Key: FalseQuestion 20 of 201.0/ 1.0 PointsThe number of car insurance policy holders is an example of a discrete random variableTrueFalse-square distributionC.F- distributionD.t -distributionQuestion 9 of 201.0/ 1.0 PointsFind the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 26 pipes has a standard deviation of 10 inches.A.14.0 < has a Y-intercept of –7.5 and a slope of 2.5, then when X = 3, the actual value of Y is:A.5B.10In C.0D.unknownQuestion 7 of 170.0/ 1.0 PointsOutliers are observations thatA.disrupt the entire linear trendB.render the study uselessIn C.lie outside the sampleD.lie outside the typical pattern of pointsQuestion 8 of 171.0/ 1.0 PointsAn agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx.Apartments.xlsxAt the .05 level of significance determine if the correlation between rental cost and apartment size is significant.A.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient 0.85 exceeds 0.50.B.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the t-test value, 7.74, is greater than the critical value 1.96.C.No, there is not a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient is less than .95.D.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the p-value for this test is less than .0001.Part 3 of 8 - 0.0/ 2.0 PointsQuestion 9 of 170.0/ 2.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the 0.10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?Pine treesSpruce treesSample size3035Mean trunk diameter (cm)4539Sample variance120140What is the test value for this hypothesis test?Test value: Correct2.474 Round your answer to three decimal places.What is the critical value?Critical value: Correct1.296 Round your answer to three decimal places.Feedback: This is a t-test of independent samples. Use the formula for the t test value on page 480:f[t=frac{(45-39)-0}{sqrt{frac{120}{30}+frac{140}{35}}}=2.121320f]Using Table F (df = 29, alpha = 0.10, one-tail test) the critical t-value is 1.311.Part 4 of 8 - 2.0/ 2.0 PointsQuestion 10 of 171.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx. Using the estimated regression equation found by using size as the predictor variable, find a point estimate for the average monthly rent for apartments having 1,000 square feet of space. Place your answer, rounded to the nearest whole dollar, in the blank. Correct1242 When entering your answer do not use any labels or symbols. Simply provide the numerical value. For example, 123 would be a legitimate entry.Apartments.xlsxQuestion 11 of 171.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsxTreating ILE as the response variable, use regression to fit a straight line to all 18 data points.Using your estimated regression output, predict the indirect labor expenses for a month in which the company has 31 direct labor hours.Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 458.9 would be a legitimate entry. Correct525.4Part 5 of 8 - 0.0/ 2.0 PointsQuestion 12 of 170.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:percent change for corporation 15 12 3 12 28 6 8 2percent change for CEO 6 17 -4 12 32 -1 7 2Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the test value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry. Correct0.357Question 13 of 170.0/ 1.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:percent change for corporation 15 12 3 12 28 6 8 2percent change for CEO 6 17 -4 12 32 -1 7 2Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the critical value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry. Correct1.773Part 6 of 8 - 1.0/ 3.0 PointsQuestion 14 of 171.0/ 3.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.A professor gives an exam for which there are two versions, A and B. Each student in the class is given one randomly selected version of the exam. After the exam, the professor wishes to determine if there is a difference in the level of difficulty of the two versions by determining if there is a significant difference in the mean scores. Assume ? = 0.05.Version AVersion BSample size4565Mean score8.88.2Sample variance2.62.4What is the test value for this hypothesis test?What is/are the critical value(s) for this hypothesis test? If there are two critical values, give only the positive value.What is the conclusion for this hypothesis test? Choose one.1. There is not sufficient evidence to show that one version of the exam is more difficult than the other.2. There is sufficient evidence to show that one version of the exam is more difficult than the other.Part 7 of 8 - 1.0/ 1.0 PointsQuestion 15 of 171.0/ 1.0 PointsIn conducting hypothesis testing for difference between two means when samples are dependent (paired samples), the variable under consideration is f$ar{D}f$ ; the sample mean difference between the pairs.CorrectTrueFalsePart 8 of 8 - 2.0/ 2.0 PointsQuestion 16 of 171.0/ 1.0 PointsIn a simple regression analysis, if the standard error of estimate sest = 15 and the number of observations n = 10, then the sum of the residuals squared must be 120.TrueFalseQuestion 17 of 171.0/ 1.0 PointsIn a simple linear regression problem, the least squares line is y' = -3.2 + 1.3X, and the coefficient of determination is 0.7225. The coefficient of correlation must be –0.85.TrueFalsemidtermQuestion 1 of 251.0/ 1.0 PointsIf you classified the fruit in a basket as apple, orange, or banana, this would be an example of which level of measurement?A.intervalB.ordinalC.ratioD.nominalPart 2 of 9 - 2.0/ 2.0 PointsQuestion 2 of 251.0/ 1.0 PointsIf two events are mutually exclusive, what is the probability that one or the other occurs?A.0.25B.Cannot be determined from the information given.C.0.50D.1.00Question 3 of 251.0/ 1.0 PointsThe staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?A.5/8B.2/5C.1/8D.1/4Part 3 of 9 - 2.0/ 3.0 PointsQuestion 4 of 251.0/ 1.0 PointsA die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled.A.60B.50C.7.1D.5.9Question 5 of 251.0/ 1.0 PointsA researcher surveyed college students to study their opinion about the proposed change in smoking rules. The researcher asked a group of 30 students: 12 of them supported the change, 13 of them did not, and 5 had no opinion. This is not a binomial model because...A....the students who strongly supported the change and those who only mildly supported the change are counted the same.B....less than half of the students supported the change.C.30 students are not enough for a good sampleD....there are 3 possible outcomes, not 2.Question 6 of 250.0/ 1.0 PointsSuppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.What is the probability that greater than 30 batteries will last at least 8 hours?In A.0.0848B.0.9152C.0.8594D.0.9522Part 4 of 9 - 5.0/ 6.0 PointsQuestion 7 of 251.0/ 1.0 PointsOne reason for standardizing random variables is to measure variables with:A.different mea0.0/ 1.0 PointsA random variable X is normally distributed with a mean of 100 and a variance of 25. Given that X = 110, its corresponding Z- score is 0.40.InTrueFalseQuestion 25 of 251.0/ 1.0 PointsIf Z is a standard normal variable, then P(Z = 1) = 0.3413.TrueFalsefinalQuestion 1 of 23 1.0/ 1.0 PointsA company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.MachineShift A B C D1 41 20 12 162 31 11 9 143 15 17 16 10A.The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.B.The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.C.The number of breakdowns is dependent on the shift, because the p-value is .07.D.The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.Question 2 of 23 1.0/ 1.0 PointsThe data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?Seed Type Observed FrequenciesGerminated Failed to Germinate1 31 72 57 333 87 604 52 445 10 19A.Yes, because the test value 16.86 is greater than the critical value of 13.28B.Yes, because the test value 16.86 is less than the critical value of 14.86C.No, because the test value 16.86 is greater than the critical value of 13.28D.No, because the test value 13.28 is less than the critical value of 16.86Part 2 of 16 - 3.0/ 3.0 PointsQuestion 3 of 23 1.0/ 1.0 PointsIn a simple linear regression analysis, the following sum of squares are produced:= 500= 100= 400The proportion of the variation in Y that is explained by the variation in X is:A.25%B.80%C.50%D.20%Question 4 of 23 1.0/ 1.0 PointsIn regression analysis, the variable we are trying to explain or predict is called theA.dependent variableB.independent variableC.regression variableD.residual variableQuestion 5 of 23 1.0/ 1.0 PointsIn choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the:A.smallest sum of squared residualsB.largest number of points on the lineC.smallest number of outliersD.largest sum of squared residualsPart 3 of 16 - 2.0/ 2.0 PointsQuestion 6 of 23 1.0/ 1.0 PointsMultiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.Patient 1 2 3 4 5 6 7Before 158 189 202 353 416 426 441After 284 214 101 227 290 176 290Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?A.t = 2.7234B.p = 2.7234C.z = 1.8424D.t = 1.8424Question 7 of 23 1.0/ 1.0 PointsMultiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.Patient 1 2 3 4 5 6 7Before 158 189 202 353 416 426 441After 284 214 101 227 290 176 290Suppose you wanted to conduct a test of hypothesis to determine if there is sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the p-value associated with the test of hypothesis you would conduct?A.p = .942597B.p = .057493C.p = .114986D.p = .885014Part 4 of 16 - 2.0/ 3.0 PointsQuestion 8 of 23 0.0/ 1.0 PointsA lab technician is tested for her consistency by taking multiple measurements of cholB.1400C.1250D.1100Part 6 of 16 - 1.0/ 1.0 PointsQuestion 13 of 23 1.0/ 1.0 PointsIf the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?A.equal to the meanB.to the left of the meanC.to the right of the meanD.one standard deviation higher than the meanPart 7 of 16 - 1.0/ 1.0 PointsQuestion 14 of 23 1.0/ 1.0 PointsIn a small town, 60% of the households have dogs. If 5 households are randomly selected, what is the probability that at least 4 of them have dogs?A.0.337B.3C.0.8D.0.259Part 8 of 16 - 1.0/ 1.0 PointsQuestion 15 of 23 1.0/ 1.0 PointsIf events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal toA.0.0B.1.0C.0.5D.any value between 0.5 and 1.0Part 9 of 16 - 3.0/ 3.0 PointsQuestion 16 of 23 3.0/ 3.0 PointsAccepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent.Sport Preferences of Men and WomenBasketball Football SoccerM

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