Question

Many years ago, the proportion of citizens of Japan who were over 65 years old was 0.16. Demographers would like to know if the proportion is greater now. A random sample of n = 80 Japanese citizens yielded 20 who were over 65.

35a

Write the null and alternative hypothesis.

35b

a = .02S. Draw a picture of the rejection region on the appropriate curve.

35c

Compute the test statistic.

35d

What is your conclusion?

35e

Draw a picture and find the p-value.

Hint: remember this rule: H0 is rejected iff p-value < a

Answer 1

Given : Sample size=n=80

Let , X be the number of citizens who are over 65.

Since , X=20

The sample proportion , p=X/n=20/80=0.25

a) Hypothesis : Vs

b) Since , Significance level=

c) The test statistic is ,

P-value :

Decision : Here , P-value = 0.0139 <

Therefore , reject Ho at significance level.

d) Conclusion : Hence , there is sufficient evidence to conclude that the proportion of citizens of Japan who were over 65 years old is greater now.