Question

9. 16 pts) Google wants to know if there is strong evidence that more than 25% of smartphone users actively use Twitter. Use the sample data to perform the hypothesis test at the 1% significance level. For full credits, you need to specify the null and alternative hypotheses, appropriate test- statistic value, p- value and conclusion Parameter to be tested: HO: Test-statistics: P-value: Conclusion:

Answer 1

The parameter to be tested is Proportion

The null and the alternative hypothesis are

and

The sample proportion is $\hat{p}={124 \over 425}\approx 0.292$

Value of test static is

$z={\hat{p}-p\over \sqrt{p(1-p)\over n}}={0.292-0.25\over \sqrt{0.25(1-0.25)\over 425}}\approx 2$

The test is right tailed test, So

P-value is $\Pr(z>2)=0.0228$

As P-value is 0.0228> 0.01

So we fail to reject the null hypothesis

Not enough evidence to support the claim.