Question

An economist claims that 40% of Americans older than 65 work part time. A sample of 200 Americans older than 65 showed 100 worked part time. Can you prove, at 95% confidence, that the economist’s claim is not true? Before doing the problem, you must show that the problem meets the requirements for performing the test. To get full credit, state your null and alternate hypothesis, show how you calculated your test statistic, show your critical region (reject region), and state your conclusion: could the economist’s claim be true?    YES   or NO

show steps in Ti84 if applicable

Answer 1

Ans:

For Ti-84,use 1-PropZTest command,enter x=100,n=200,choose two sided alternative,confidence,c=0.95 and calculate.

(Claim)

sample proportion=100/200=0.5

Test statistic:

z=(0.50-0.40)/sqrt(0.40*(1-0.40)/200)

z=2.89

p-value(2 tailed)=2*P(z>2.89)=0.00385

As,p-value<0.05,we reject the null hypothesis.

No,the economist’s claim can not be true.