Question

In a certain​ survey, 501 people chose to respond to this​ question: "Should passwords be replaced with biometric security​ (fingerprints, etc)?" Among the​ respondents, 52​% said​ "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Complete parts​ (a) through​ (d) below.

a. Are any of the three requirements​ violated? Can a test about a population proportion using the normal approximation method be​ used?

A. The conditions npgreater than or equals5 and nqgreater than or equals5 are not​ satisfied, so a test about a population proportion using the normal approximation method cannot be used.
B. One of the conditions for a binomial distribution are not​ satisfied, so a test about a population proportion using the normal approximating method cannot be used.
C. All of the conditions for testing a claim about a population proportion using the normal approximation method are​ satisfied, so the method can be used. Your answer is not correct.
D. The sample observations are not a random​ sample, so a test about a population proportion using the normal approximating method cannot be used.

b. It was stated that we can easily remember how to interpret​ P-values with​ this: "If the P is​ low, the null must​ go." What does this​ mean?

A. This statement means that if the​ P-value is very​ low, the null hypothesis should be accepted.
B. This statement means that if the​ P-value is not very​ low, the null hypothesis should be rejected.
C. This statement means that if the​ P-value is very​ low, the alternative hypothesis should be rejected.
D. This statement means that if the​ P-value is very​ low, the null hypothesis should be rejected.

c. Another memory trick commonly used is​ this: "If the P is​ high, the null will​ fly." Given that a hypothesis test never results in a conclusion of proving or supporting a null​ hypothesis, how is this memory trick​ misleading?

A. This statement seems to suggest that with a high​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made.
B. This statement seems to suggest that with a high​ P-value, the alternative hypothesis has been proven or is​ supported, but this conclusion cannot be made.
C. This statement seems to suggest that with a high​ P-value, the alternative hypothesis has been​ rejected, but this conclusion cannot be made.
D. This statement seems to suggest that with a low​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made.

d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like​ 0.0483?

A. Choosing a more specific significance level will make it more difficult to reject the null hypothesis.
B. Choosing this specific of a significance level could give the impression that the significance level was chosen specifically to reach a desired conclusion.
C. A significance level with more than 2 decimal places has no meaning.
D. Significance levels must always end in a 1 or a 5.

Answer 1

1)  The sample observations are not a random​ sample, so a test about a population proportion using the normal approximating method cannot be used. OPTION D

2) This statement means that if the​ P-value is very​ low, the null hypothesis should be rejected OPTION D

3) This statement seems to suggest that with a high​ P-value, the null hypothesis has been proven or is​ supported, but this conclusion cannot be made. OPTION A

4) Choosing this specific of a significance level could give the impression that the significance level was chosen specifically to reach a desired conclusion. OPTION B