Question

Assume a significance level of α=0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: More than 49​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.0281.

Required:
a. State a conclusion about the null hypothesis.​
b. Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?

1. The percentage of adults that would erase all of their personal information online if they could is more than or equal to 49​%.
2. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 49​%.
3. There is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 49​%.
4. The percentage of adults that would erase all of their personal information online if they could is less than 49​%.

Answer 1

Part a: The correct answer is A, reject H0 because p value is less than . Part B: The correct answer is C, the percentage of adults that would erase their personal information online if they could is more than 51%.

Explanation:

part a. The essential idea of hypothesis testing in statistics is to evaluate the probability p (p value) of some representative parameter, compared to a level of likelihood that is set before starting the test (). In this case, we are interested in a level of likelihood , which means that if the probability of the parameter is less than 5%, we will reject the hypothesis that this parameter is representing, since it's so unlikely. Of course, the significance level is arbitrary and must be payed attention, according to the particular situation. Therefore, the correct anser is A.

part b. Since we rejected the hypothesis to a 5% significance level, we reject the fact that less than 51% of adults would erase their personal information online if they could. This is equivalent to saying that a percentage of adults equal to or more than 51% would erase their personal information if they