# UMUC STAT200 test 1 and test 2 latest 2015 november

Question

UMUC STAT-200 Test #1

Instructions: Students must complete the quiz, on their own, with no help from other students, though help from your instructor is allowed. Students may use their books, computers and any other online resources to complete the quiz. Students must submit their answers and detailed work in a WORD or PDF attachment in the assignments area before the deadline on Sunday at 12-midnight. All work must be shown to receive full credit for a solution. Submitting an answer without any supporting information or explanation, will not receive credit. In some cases no supporting information or explanation is needed, but in many cases, an explanation of how the answer was obtained is needed. Please use your judgment in providing supporting information for your solutions. It is strongly suggested that students DO NOT wait until Sunday afternoon to start their quiz. Late tests will be penalized 10% per day.

Course Material: Covers material from weeks 1,2,3

Scoring: Each problem is worth 10 points. Some problems contains multiple parts, but the total value of the problem will be 10 points. The total test score will be a maximum of 100 points.

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(Problem 1) A random sample of 12 customers was chosen in a supermarket. The (incomplete) results for their checkout times are shown in the table below.

Checkout Time (minutes)

Frequency

Relative Frequency

Cumulative Relative Frequency

4.0 – 5.9

2

6.0 – 7.9

0.25

8.0 – 9.9

10.0 – 11.9

1

12.0 – 13.9

2

TOTALS

12

(a – 4 points) Complete the frequency table

(b – 2 points) What percent of the checkout times are at least 10 minutes?

(c – 2 points) What percent of the checkout times are between 8 and 10 minutes?

(d – 2 points) What percent of the checkout times are less than 12 minutes?

(Problem 2) Using the data from Problem #1 …

(a – 4 points) Construct a histogram

(b – 2 points) In what class interval must the median lie?

Assume the largest recorded checkout time was 13.2 minutes. Suppose that data point was incorrect and the actual checkout time was 13.8 minutes.

(c – 2 points) Will the mean of the dataset increase, decrease or remain the same and why?

(d – 2 points) Will the median of the dataset increase, decrease or remain the same and why?

(Problem 3) A fitness center is interested in the mean amount of time the clients exercise each week. A survey will be conducted of the clients. Answer the following questions (2 points each).

(a) What is the population?

(b) What is the sample?

(c ) What is the parameter?

(d) What is the statistic ?

(e) What is the variable?

(Problem 4) A random sample of starting salaries for an engineer are: $38000, $42000, $44000, $48000, and $68000. Find the following and show all work (2 points each). Include equations, a table or EXCEL work, to show how you found your solution.

(a) Mean

(b) Median

(c) Mode

(d) Standard Deviation

(e) If a recent graduate is considering a career in engineering, which statistic (mean or median) should they consider when determining the starting salary they are likely to make? Explain your answer.

(Problem 5) The checkout times (in minutes) for 12 randomly selected customers at a large supermarket during the store’s busiest time are as follows: 4.6, 8.5, 6.1, 7.8, 10.7, 9.3, 12.4, 5.8, 9.7, 8.8, 6.7, 13.2

(a – 2 points) What is the mean checkout time?

(b – 2 points) What is the value for the 25% percentile (first quartile) Q1?

(c – 2 points) What is the value for the 50% percentile (median)?

(d – 2 points) What is the value for the 75% percentile (third quartile) Q3?

(e – 2 points) Construct a boxplot of the dataset.

(Problem 6) Roll two fair dice. Each die has six faces.

(a – 2 points) List the number of outcomes in the sample space

(b – 2 points) What is the probability of rolling a 2 or a 5 on the first roll?

(c – 2 points) What is the probability of rolling a 2 or 5 and then an ODD number?

(d – 2 points) What is the probability the sum of the rolls is less than 4?

(e – 2 points) What is the probability that the second roll is greater than 4, given that the first roll is an even number?

(Problem 7) In a box of 100 cookies, 36 contain chocolate and 12 contain nuts. Of those, 8 cookies contain both chocolate and nuts.

(a – 3 points) Draw a Venn diagram representing the sample space and label all regions

(b – 1 points) What is the probability that a randomly selected cookie contains chocolate?

(c – 3 points ) What is probability that a randomly selected cookie contains chocolate OR nuts? Note, it cannot contain both chocolate and nuts, but must have either chocolate OR nuts.

(d – 3 points) What is the probability that a randomly selected cookie contains nuts, given that it contains chocolate?

(Problem 8)Assume a baseball team has a lineup of 9 batters.

(a – 4 points) How many different batting orders are possible with these 9 players?

(b – 4 points) How many different ways can I select the first 3 batters?

(c – 2 points) Is a “Combination Lock” really a permutation or combination of numbers? Explain your answer.

(Problem 9) You are playing a game with 3 prizes hidden behind 5 doors. One prize is worth $100, another is worth $20 and another $10. You have to pay $20 if you choose a door with no prize.

(a – 4 points) Construct a probability table. See your homework for Illowsky, Chapter 4, #72 and #80.

(b – 3 points) What is your expected winning?

(c – 3 points) What is the standard deviation of your winning?

(Problem 10) Suppose that 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen. Let X be the number of students that attend graduation. As we know, the distribution of X is a binomial probability distribution. Answer the following:

(a – 1 point) What are the number of trials (n)?

(b – 1 point) What is the probability of successes (p)?

(c – 1 point) What is the probability of failures (q)?

(d – 2 points) How many students are expected to attend graduation?

(e – 5 points) What is the probability that 18 students attend graduation?

.0001pt; text-indent: 0cm;”>UMUC STAT-200 Test #2

Dr. Brian Killough

Instructions: Students must complete the quiz, on their own, with no help from other students, though help from your instructor is allowed. Students may use their books, computers and any other online resources to complete the quiz. Students must submit their answers and detailed work in a WORD or PDF attachment in the assignments area before the deadline on Sunday at 12-midnight. All work must be shown to receive full credit for a solution. Submitting an answer without any supporting information or explanation, will not receive credit. In some cases no supporting information or explanation is needed, but in many cases, an explanation of how the answer was obtained is needed. Please use your judgment in providing supporting information for your solutions. It is strongly suggested that students DO NOT wait until Sunday afternoon to start their quiz. Late tests will be penalized 10% per day.

Course Material: Covers material from weeks 4,5,6

Scoring: The total test score will be a maximum of 100 points. Points vary and are noted for each problem.

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(Problem 1) TRUE or FALSE. Explain your answer for full credit. (2 points each, 10 points total)

(a) In a normal distribution, 68% of the area under the curve is within one standard deviation of the mean.

(b) Given that a normal distribution has a mean of 50 and standard deviation of 5. The median is also 50.

(c) If the variance from a set of data is zero, then all of the data values must be identical.

(d) A 95% confidence interval is wider than and 99% confidence interval of the same parameter. (e) It is easier to reject the null hypothesis if we a smaller significance level (?).

(Problem 2) The patient recovery time from a surgical procedure is normally distributed with a mean of

5.3 days and standard deviation of 2.1 days. (5 points each, 10 points total)

(a) What is the probability of spending more than 2 days in recovery after a surgical procedure? (b) What is the 90th percentile for recovery time after a surgical procedure?

(Problem 3) Human heights are known to be normally distributed. Men have a mean height of 70 inches and females a mean height of 64 inches. Both have a standard deviation of 3 inches. (3 points each, 15 points total)

(a) Find the 1st Quartile (Q1) of the female height distribution

(b) Find the height of a female in the 90th percentile

(c) What is the probability that a randomly selected female is above 70 inches height?

Assume a random sample of 100 males is selected.

(d) What is the standard deviation of the sample mean?

(e) What is the probability that the mean height of samples is less than 68 inches tall

(Problem 4) The average height of students has a normal distribution with a standard deviation of 2.5 inches. You want to estimate the mean height of students at your college to within 1-inch with 95% confidence. How many students should you measure? HINT: Be sure to consider the two-tail probability when evaluating the z-score for the confidence level. (10 points)

(Problem 5) A random sample of 150 test scores has a sample mean of 80. Assume that the test scores have a population standard deviation of 15. Construct a 95% confidence interval estimate of the mean test scores. (10 points)

(Problem 6)A statistics instructor believes that 50% of his students are male. One of his students thinks there are more males than females taking statistics, so he decides to conduct a random survey of past courses. He found that 83 of 150 students were male. Answer the questions below. HINT: This is a test of a single population proportion. See Example 9.17 on page 487 of the textbook. (3 points each, 15 points total)

(a) What is the null hypothesis (Ho) and what is the alternate hypothesis (Ha)?

(b) What is the standard error of the proportion?

(c) What is the test statistic?

(d) What is the P-value for this test? HINT: Assume a normal distribution and use the single population proportion equations on page-502 of Illowsky.

(e) Is there sufficient evidence to reject the null hypothesis (Ho) at a 99% confidence level (?=0.01)?

(Problem 7) Taking an SAT preparatory course is believed to improve test scores. To investigate the effects of taking a preparatory course, scores were recorded for 5 students before and and after they took the preparatory course. Does the data below suggest that a preparatory course increases test scores? Assume we want a 90% confidence level (?=0.10) to test the claim. HINT: Assume the null hypothesis is that test scores stay the same, before and after taking the course. Also, assume the “expected” change in test scores is zero when evaluating the test statistic. (3 points each, 15 points total)

(a) Identify the alternate hypothesis

(b) What is the random variable (X) that we want to evaluate?

(c) Find the test statistic (show all work)

(d) Find the P-value (show all work)

(e) Is there sufficient evidence to support the claim that taking a preparatory course increases an SAT test score? Justify your conclusion.

Student

Before

After

1

1200

1260

2

1150

1120

3

1260

1260

4

1050

1200

5

980

1050

(Problem 8) Researchers interviewed young adults in Canada and the U.S to compare their ages when they enter the workforce. The mean age of the 100 Canadians was 18 with a standard deviation of 6. The mean age of the 130 people interviewed in the U.S. was 20 with a standard deviation of 8. Is the mean age of entering the workforce in Canada lower than the mean age in the U.S.? (5 points each, 15 points total)

(a) Identify the null and alternate hypothesis

(b) Find the test statistic (show all work). HINT: You are testing two population means with known standard deviations. See the equation on page-554.

(c) Find the P-value (show all work) and evaluate whether the mean age of entering the workforce in Canada is lower than the mean age in the U.S.? Test at a 1% significance level.

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