Question

8. A researcher claims that more than 35% of U.S. adults have been a victim to identity theft. In a random sample of 490 U.S. adults, 192 of them have been a victim to identity theft.

a) Is there enough evidence to support the researchers claim at the 1% level of significance?

b) Is there enough evidence to support the claim at the 10% level of significance?

Answer 1

Total number of sample (n) = 490
number of favourable events (X) = 192

We are interested in testing the hypothesis


Since, the test is two-tail test at \alpha = 0.01

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 2.3263
The statistic value, 1.9416 is less than the critical values 2.3263. Therefore, we fail to reject the null hypothesis.


We are interested in testing the hypothesis

Since, the test is two-tail test at \alpha = 0.1

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.28
The statistic value, 1.9416 is greater than the critical value 1.28. Hence, reject the null hypothesis.