Question

A researcher believes that the percentage of people who smoke in the South is greater than in the nation as a whole. The national rate is 15%. The researcher gathers a random sample of 110 individuals who live in the South and finds that the number who smoke is 21 out of 110.

Use the x2 goodness-of-fit test

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

Answer 1

Ans:

a)One sample proportion z test

b)

c)sample proportion=21/110=0.1909

Test statistic:

z=(0.1909-0.15)/sqrt(0.15*(1-0.15)/110)

z=1.20

p-value=P(z>1.20)=0.1150

d)

As,p-value>0.05,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the percentage of people who smoke in the South is greater than in the nation as a whole