A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age:
x1: Rate of hay fever per 1000 population for people under 25

A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old:
x2: Rate of hay fever per 1000 population for people over 50

Use a calculator to verify that 1 ‰ˆ 109.50, s1 ‰ˆ 15.41, 2 ‰ˆ 99.36, and s2 ‰ˆ 11.57.
(a) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use α = 0.05.
(b) Find a 90% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) €“ (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.

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