**For each problem, include the relevant SAS output by copying and pasting it into your WORD document before you convert it to a .PDF. **

**For each hypothesis test, state the null and alternative hypotheses and give the significance level, value of the test statistic, and p-value. State whether you would reject or fail to reject the null hypothesis and give a conclusion in “layman’s terms,” i.e., use wording that would be understandable to someone who does not know any statistical jargon.**

**For any hand calculations, be sure to show how you got your answer; otherwise, we will not be able to give you partial credit if you get the final answer wrong.**

**1. **Consider Exercise 22, p. 207, of our textbook. Using the data given in this exercise, use SAS Studio to answer each of the following questions. The data can be found in hwk3p1 in your MYDATA library. Assume that pH level is normally distributed.

a. A salivary pH of 7.4 or more is considered “normal.” pH levels smaller than this can lead to increased risk of cavities (dental caries). Let µA and µB denote the true population mean pH of caries-free 7th graders (Group A) and caries-prone 7th graders (Group B), respectively. Test the following hypotheses:

i. H0: µA ≥ 7.4 vs. HA: µA < 7.4

ii. H0: µB ≥ 7.4 vs. HA: µB < 7.4.

b. Find and interpret a 95% confidence interval for both µA and µB. Use these confidence intervals to test the null hypotheses H0: µA = 7.4 and H0: µB = 7.4.

c. Use a two-sample t-test to test the following hypotheses:

H0: µA = µB vs. HA: µA = µB

d. Find and interpret a 95% confidence interval for µA – µB. Use this confidence interval to test the null hypothesis in part c. above.

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MUST INCLUDE SCREENSHOTS FROM SAS AND any hand calculations WITH WORK SHOWN

DATA SET:

From book:

Determinations of saliva pH levels were made in two independent Random Samples of seventh-grade schoolchildren. Sample A children were caries free while sample B children had a high incidence of caries. The results were as follows:

A 7.14, 7.11, 7.61, 7.98, 7.21, 7.16, 7.89, 7.24, 7.86, 7.47, 7.82, 7.37, 7.66, 7.62, 7.65

B 7.36, 7.04, 7.19, 7.41, 7.10, 7.15, 7.36, 7.57, 7.64, 7.00, 7.25, 7.19

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