# Statistics questions

1. The U.S. Census Bureau collects data on the ages of married people. Suppose that eight married couples are randomly selected and have the ages given in the following table. Determine the confidence interval for the true mean difference between the ages of married males and married females.

Let (age of husband) (age of wife). Assume that the ages are normally distributed for the populations of both husbands and wives in the U.S.

Husband

Wife

Step 1 of 4:

Find the mean of the paired differences, . Round your answer to one decimal place.

Answer :

Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer :

Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place.

Answer :

Step 4 of 4: Construct the confidence interval. Round your answers to one decimal place.

Lower endpoint: Upper endpoint:

2. A publisher reports that of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of found that of the readers owned a personal computer. Is there sufficient evidence at the level to support the executive’s claim? Step 1 of 6: State the null and alternative hypotheses.

:

:

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

98%

d = −

60 71 24 32 45 28 60 51

68 70 30 44 36 39 67 62

d ¯̄̄

98%

56% 160 48%

0.02

H 0

H a

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Step 3 of 6: Specify if the test is one-tailed or two-tailed.

One-Tailed Test

Two-Tailed Test

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, .

Reject if

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

Step 6 of 6: State the conclusion of the hypothesis test.

3. A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students’ attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of nursing students from Group 1 resulted in a mean score of with a standard deviation of . A random sample of nursing students from Group 2 resulted in a mean score of with a standard deviation of . Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let represent the mean score for Group

1 and represent the mean score for Group 2. Use a significance level of for the test. Assume that the population

variances are equal and that the two populations are normally distributed. Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to three decimal places.

A )

B )

H 0

H 0

∣ z ∣ >

A )

B )

A ) There is sufficient evidence to support the claim that the percentage of readers who own a personal computer is different from .56%

B ) There is not sufficient evidence to support the claim that the percentage of readers who own a personal computer is different from .56%

11 56.3 6.1 6 64.1 6.5

µ 1

µ 2

α = 0.01

:H 0

µ 1

µ 2

:H a

µ 1

µ 2

t

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Step 3 of 4:

Determine the decision rule for rejecting the null hypothesis . Round your answer to three decimal places.

Reject if

Step 4 of 4: State the test’s conclusion.

Reject Null Hypothesis Fail to Reject Null Hypothesis

4. Using traditional methods it takes hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on students and observed that they had a mean of hours. Assume the population variance is known to be . Is there evidence at the level that the technique lengthens the training time? Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

One-Tailed Test

Two-Tailed Test

Step 4 of 6: Find the -value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

H 0

H 0

A ) B )

107 150 108

25 0.01

:H 0

:H a

A )

B )

P

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Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

5. An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of lbs/square inch. The valve was tested on engines and the mean pressure was lbs/square inch. Assume the variance is known to be . Is there evidence at the level that the valve performs above the specifications? Step 1 of 5: Enter the hypotheses:

Step 2 of 5: Enter the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

One-Tailed Test

Two-Tailed Test

Step 4 of 5: Enter the decision rule.

Reject if

Step 5 of 5: Enter the conclusion.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

6. Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of samples is ppm with a standard deviation of . Does the data support the claim at the level? Assume the population distribution is approximately normal.

A )

B )

4.8 140 5.0 0.64 0.1

:H 0

:H a

z

A )

B )

H 0

z >

A )

B )

6.6 24 6.9

0.7 0.01

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Step 1 of 5: State the null and alternative hypotheses.

Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.

Answer :

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

One-Tailed Test

Two-Tailed Test

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Reject if

Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

7. Consider the following table:

SS DF MS

Among Treatments

Error

Total

Step 1 of 8: Calculate the sum of squares among treatments. Please round your answer to two decimal places.

:H0

:Ha

A )

B )

H0 t >

A )

B )

F

? 2 1189.32

357.14

5950.04 12

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Step 2 of 8: Calculate the sum of squares of experimental error. Please round your answer to two decimal places.

Step 3 of 8: Calculate the degrees of freedom of experimental error.

Step 4 of 8: Calculate the -value. Please round your answer to two decimal places.

Step 5 of 8: What is the sum of squares of sample means about the grand mean? Please round your answer to two decimal places.

Step 6 of 8: What is the variation of the individual measurements about their respective means? Please round your answer to two decimal places.

Step 7 of 8: What is the critical value of at the level? Please round your answer to four decimal places, if necessary.

Step 8 of 8: Is significant at ?

Yes No

8. The director of research and development is testing a new drug. She wants to know if there is evidence at the level that the drug stays in the system for less than minutes. For a sample of patients, the mean time the drug stayed in the system was

minutes. Assume the population standard deviation is .

F

F 0.1

F 0.1

A ) B )

0.05 386 78

383 22

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Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

One-Tailed Test

Two-Tailed Test

Step 4 of 6: Find the -value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

9. A publisher reports that of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually above the reported percentage. A random sample of found that of the readers owned a particular make of car. Is there sufficient evidence at the level to support the executive’s claim? Step 1 of 6: State the null and alternative hypotheses.

:

:

:H 0

:H a

A )

B )

P

A )

B )

54% 200 61%

0.02

H 0

H a

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Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

One-Tailed Test

Two-Tailed Test

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, .

Reject if

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

Step 6 of 6: State the conclusion of the hypothesis test.

A )

B )

H 0

H 0

z >

A )

B )

A ) There is sufficient evidence to support the claim that the percentage of readers who own a particular make of car is above .54%

B ) There is not sufficient evidence to support the claim that the percentage of readers who own a particular make of car is above .54%

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