MA260 Online Exam 8_07 December 2015 Solution

| August 30, 2017

Question
Online Exam 8_07

Question 11 of 40

2.5 Points

A study of a brand of “in the shell peanuts” gives the following results:

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A significant event at the 0.01 level is a fan getting a bag with how many peanuts?

A. 30 peanuts

B. 25 or 30 peanuts

C. 25 or 55 peanuts

D. 25 peanuts

Question 12 of 40

2.5 Points

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of significance.

A.

H0: p = 0.001 Ha: p > 0.001

B.

H0: p = 0.001 Ha: p 0.001 Ha: p = 0.001

D.

H0: p < 0.001 Ha: p = 0.001

Question 13 of 40

2.5 Points

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.

A. Conclusion: Support the claim that the mean is less than 9.4 minutes.

B. Conclusion: Support the claim that the mean is greater than 9.4 minutes.

C. Conclusion: Support the claim that the mean is equal to 9.4 minutes.

D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.

Question 14 of 40

2.5 Points

The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by s = $13,700. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

A. The current seventh graders at the principal’s school

B. Seventh graders’ families at the school with a standard deviation of $13,700

C. All of the families of the class of seventh graders at the principal’s school

D. All seventh graders’ families

Question 15 of 40

2.5 Points

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler.

Determine the null and alternative hypotheses for the test described.

A.

H0: µ = 16 ounces Ha: µ 16 ounces

D.

H0: µ = 16 ounces Ha: µ ¹ 16 ounces

Question 16 of 40

2.5 Points

The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.

A. There is sufficient evidence to support the claim that the mean attendance is greater than 3000.

B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.

C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.

D. There is not sufficient evidence to support the claim that the mean attendance is less than 3000.

Question 17 of 40

2.5 Points

A supplier of DVDs claims that no more than 1% of the DVDs are defective. In a random sample of 600 DVDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier’s claim that no more than 1% are defective.

A. Do not reject the null hypothesis and conclude that there is evidence to support the claim that more than 1% of the DVDs are defective.

B. Reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.

C. Do not reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.

D. Reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 1% of the DVDs are defective.

Question 18 of 40

2.5 Points

In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:

H0 : µ = 9.8 hours

Ha : µ > 9.8 hours

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.

A. Type I error

B. Type II error

C. Correct decision

D. Can not be determined from this information

Question 19 of 40

2.5 Points

A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?

A. Greater than or equal to 0.10

B. Less than or equal to 0.05

C. Less than or equal to 0.10

D. Greater than or equal to 0.05

Question 20 of 40

2.5 Points

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 0.02 level of significance. The mean acetaminophen content for a random sample of n = 41 tablets is 603.3 mg. Assume that the population standard deviation is 4.9 mg.

A. Since the test statistic is greater than the critical z, there is sufficient evidence to accept the null hypothesis and to support the claim that the mean content of acetaminophen is 600 mg.

B. Since the test statistic is greater than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

C. Since the test statistic is less than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

D. Since the test statistic is greater than the critical z, there is insufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

Question 21 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.

The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 4.613, state your conclusion about the relationship between gender and colorblindness.

A.

Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

B.

Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

C.

Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

D.

Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

Question 22 of 40

2.5 Points

A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed.

Data from this test resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.

Area in one tail

0.025 0.05

Area in two tails

Degrees of

Freedom

n – 1 0.05 0.10

6 2.447 1.943

7 2.365 1.895

8 2.306 1.860

9 2.262 1.833

A.

Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.

B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.

C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.

D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.

Question 23 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 8 52 60

Female 2 38 40

Total 10 90 100

State the null and alternative hypothesis for the test associated with this data.

A.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are not related in any way.

B.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are related in some way.

C.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are not related in any way.

D.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are related in some way.

Question 24 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 8 52 60

Female 2 38 40

Total 10 90 100

Find the value of the X2 statistic for the data above.

A. 1.463

B. 1.852

C. 1.947

D. 1.949

Question 25 of 40

2.5 Points

Which of the following statements is true?

A. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

B. The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

C. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

D. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

Question 26 of 40

2.5 Points

The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.

A. Smaller. E decreases as the square root of the sample size gets larger.

B. Smaller. E increases as the square root of the sample size gets larger.

C. Larger. E decreases as the square root of the sample size gets larger.

D. Larger. E increases as the square root of the sample size gets larger.

Question 27 of 40

2.5 Points

Which of the following statements is true?

A. The p distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

B. The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

C. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

D. The p distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

Question 28 of 40

2.5 Points

The __________ test statistic is for the one-way analysis of variance.

A. P-Value

B. t

C. F

D. p

Question 29 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.

The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 3.179, state your conclusion about the relationship between gender and colorblindness.

A.

Do not reject H0.

B.

Reject H0.

C.

There is sufficient evidence to support the claim that gender and colorblindness are not related.

D.

There is not sufficient evidence to accept or reject H0.

Question 30 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 8 52 60

Female 2 38 40

Total 10 90 100

If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row and column totals.

Colorblind Not Colorblind Total

Male 6 54 60

Female 4 36 40

Total 10 90 100

A. Male Colorblind 6.0; Male Not Colorblind 54.0

B. Male Colorblind 7.0; Male Not Colorblind 53.0

C. Male Colorblind 8.0; Male Not Colorblind 52.0

D. Male Colorblind 6.0; Male Not Colorblind 53.0

Question 31 of 40

2.5 Points

A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?

A. 4.6

B. 4.4

C. 4.2

D. 5.6

Question 32 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 7 53 60

Female 1 39 40

Total 8 92 100

If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.

A. Colorblind Male 4.8; Not Colorblind Male 55.2

B. Colorblind Male 6.8; Not Colorblind Male 53.2

C. Colorblind Male 4.8; Not Colorblind Male 55.4

D. Colorblind Male 4.8; Not Colorblind Male 56.2

Question 33 of 40

2.5 Points

The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?

A. Smaller. E increases as the square root of the sample size gets larger.

B. Smaller. E decreases as the square root of the sample size gets larger.

C. Larger. E decreases as the square root of the sample size gets larger.

D. Larger. E increases as the square root of the sample size gets larger.

Question 34 of 40

2.5 Points

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ 180

B.

H0: µ > 180; Ha: µ > 180

C.

H0: µ 180

D.

H0: µ = 180; Ha: µ < 180

Question 38 of 40

2.5 Points

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed.

Data from this test resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below to solve this problem.

Area in one tail

0.025 0.05

Area in two tails

Degrees of

Freedom

n – 1 0.05 0.10

6 2.447 1.943

7 2.365 1.895

8 2.306 1.860

9 2.262 1.833

A.

Do not reject the null hypothesis. The data do not provide sufficient

evidence that the average distance is greater than 160 yards.

B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards.

C. t= 1.2334; Critical value = 1.992

D. Insufficient information to answer this question.

Question 39 of 40

2.5 Points

The following data were analyzed using one-way analysis of variance.

A B C

34 27 19

26 23 31

31 29 22

28 21 22

Which one of the following statements is correct?

A.

The purpose of the analysis is to determine whether the groups A, B, and C are independent.

B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.

C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.

D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

Question 40 of 40

2.5 Points

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 8, the sample mean x? is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.

A. df = 7; E = 3.344 5.38 = 5.6566

B. df = 8; E = 3.344 5.38 = 5.6566

C. df = 6; E = 2.365 6.38 = 5.769

D. df = 7; E = 2.365 6.38 = 5.869

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