Problem Set 7

You are welcome to get assistance on these problems from classmates, learning labs, tutors or me. It is also okay to double check your answers with me before submitting the Problem Set for evaluation.

1. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Construct a 95% confidence interval for the difference between the population proportions. You may assume the samples are independent.

You will be asked to identify each of the following.

1. The justification for normality in this situation.
2. The critical value needed to complete this calculation.
3. The value p-hat _20-24 – p-hat _25-29 that will be used as the point estimate for the calculation of this interval.
4. The value of E, the error found to calculate the interval.
5. The confidence interval for the mean difference between the population proportions.

B. A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. You may assume the populations are normally distributed.

Before 70 80 92 99 93 97 76 63 68 71 74

After 69 79 90 96 91 95 75 64 62 64 76

You will be asked to identify each of the following.

6. The justification for normality in this situation.

7. The critical value needed to complete this calculation.

8. The value d-bar (Before – After) that will be used as the point estimate for the calculation of this interval.

9. The value of E, the error found to calculate the interval.

10. The confidence interval for the mean difference between before and after scores.

C. A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to test the claim that the treatment population mean  ₁ is smaller than the control population mean  ₂ . Test the claim using a significance level of 0.01. You may assume the samples are independent and were randomly selected.

Treatment Group Control Group

n ₁ = 85 n ₂ = 75

x-bar ₁ = 189.1 x-bar ₂ = 203.7

s ₁ = 38.7 s ₂ = 89.2

You will be asked to identify each of the following.

11. The justification for normality in this situation.

12. The null and alternative hypotheses appropriate for this test.

13. The calculated value of the test statistic. (To match my answer you will need to take Treatment Group – Control Group.)

14. The prob-value calculated for this test.

15. The decision reached by this test.

D. A restaurant that delivers pizza wants to be sure that the delivery times remain consistent regardless of whether they have 1 or 2 delivery drivers working. Use a 0.10 significance level to determine whether or not the mean delivery times for the two different levels of staffing are essentially the same. You may assume the populations are normally distributed and that the samples are independent.

1 Driver 2 Drivers

n ₁ = 28 n ₂ = 41

x-bar ₁ = 19.2 x-bar ₂ = 23.7

s ₁ = 5.38 s ₂ = 5.89

You will be asked to identify each of the following.

16. The justification for normality in this situation.

17. The null and alternative hypotheses appropriate for this test. (To match my answer you will need to take 1 – 2.)

18. The calculated value of the test statistic. (To match my answer you will need to take 1 – 2.)

19. The critical-value needed for this test.

20. The decision reached by this test.

Each of these 20 questions will be worth 3 points.

Price: $23.43

Solution: The downloadable solution consists of 12 pages, 1143 words and 16 charts.
Deliverable: Word Document