Chapter 10.2, Problem 16P

Please provide the following information for Problems 11-22. part (a):

(i) What is the level of significance? State the null and alternate hypotheses.

(ii)Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(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 a?

(v)Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount, and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.

Medicine: Hay Fever A random sample of $n_1=16$ communities in western Kansas gave the following information for people under 25 years of age:

$x_1$: Rate of hay fever per 1000 population for people under 25

98	90	120	128	92	123	112	93
125	95	125	117	97	122	127	88

A random sample of $n_2=14$ regions in western Kansas gave the following information for people over 50 years old:

$x_2$: Rate of hay fever per 1000 population for people over 50

95	110	101	97	112	88	110
79	115	100	89	114	85	96

(Reference: National Center for Health Statistics.)

Use a calculator to verify that ${\bar{x}}_{{}_1}\approx 109.50,s_1\approx 15.41,{\bar{x}}_{{}_2}\approx 99.36,\text{ and }{s}_2\approx 11.57$

(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 $\alpha =0.05$.

(b) Find a 90% confidence interval for ${\mu }_1-{\mu }_2$. Explain the meaning of the confidence interval in the context of the problem.