In a certain survey, 509 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 55% 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.---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 alternative hypothesis has been rejected, 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 null hypothesis has been proven or is supported, 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?---Explanation:- Option C indicates the misleading nature of the memory trick, as it implies that a high P-value conclusively proves or supports the null hypothesis, which is not accurate. - The last question explores the reasoning behind selecting standard significance levels rather than arbitrary ones, ensuring consistency and comparability in hypothesis testing. In a certain survey, 509 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 55% 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 np ≥ 5 and nq ≥ 5 are not satisfied, so a test about a population proportion using the normal approximation method cannot be used.- **B.** 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.- **C.** The sample observations are not a random sample, so a test about a population proportion using the normal approximating method cannot be used.- **D.** 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.**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 not very low, the null hypothesis should be rejected.- **B.** This statement means that if the P-value is very low, the null hypothesis should be accepted.- **C.** This statement means that if the P-value is very low, the null hypothesis should be rejected.

Introduction: Denote the population proportion of people who believe passwords should be replaced with biometric security as p, the sample size as n, and the corresponding sample proportion as p̂.a. The null and alternative hypotheses to test the claim that more than half, or more than 50% (0.5 proportion) of the population believe passwords should be replaced with biometric security, are as follows: H0: p = 0.5 (or p ≤ 0.5); H1: p > 0.5. To test about the population proportion using the normal approximation, the requirements to be satisfied are: the sample units must be chosen randomly, the outcomes must be classified as success and failure with a constant probability of success p for each trial, and np ≥ 5, nq ≥ 5 where q = 1 – p is the probability of failure. In this case, the sample size is, n = 509, and the hypothesized probability of success or hypothesized proportion of the population believe passwords should be replaced with biometric security is, p = 0.5. Note that, q = 1 – p = 1 – 0.5 = 0.5. Therefore, np = 509 × 0.5 = 254.5 > 5, nq = 509 × 0.5 = 254.5 > 5. However, it is mentioned that the 509 people participating in the study are those who chose to respond to the question. When a participant themselves chooses to respond to a study, the sampling type is a voluntary response sampling, where the researchers are unable to choose individuals randomly from the population as desired. Clearly, here, the sample observations are not a random sample, so that the normal approximation method for testing about the population proportion cannot be used. Option C is the correct choice.b. The decision rule using the P-value is that, if the P-value is less than the significance level, then the null hypothesis must be rejected, where the significance level is a predetermined, usually small probability value, such as 0.001, 0.01, 0.05, 0.10, etc. Whatever be the particular significance level for the test, if the P-value for the test is less than that significance level, then the null hypothesis should be rejected. If the P-value is very small, it will be lower than most significance levels. In that case, the null hypothesis will be rejected. In the quoted statement, "the null must go" indicates that the null hypothesis must be let go of, or rejected. Thus, the given statement means that, if the P-value is very low, the null hypothesis should be rejected. Options A, B, and D are not appropriate, and option C is not visible in the image.c. Using the same decision rule, if the P-value is large, it will be greater than most significance levels. In that case, the null hypothesis will not be rejected, or fail to be rejected. In the quoted statement, "the null will fly" seems to suggest that the null hypothesis can be taken to be true, or accepted. However, in a hypothesis testing problem, the hypotheses are so constructed that the null can be rejected while accepting the alternative, or the null can fail to be rejected while failing to find evidence for the alternative. Thus, even though the quoted statement seems to suggest so, there is no scope of accepting the null hypothesis is a traditional hypothesis testing setup. Thus, the given statement seems to suggest that, if the P-value is high, the null hypothesis has been proven or supported, but such a conclusion cannot be made. Option C is correct.d. Recall that the decision rule is to reject the null hypothesis if the P-value is less than the significance level, and there are some commonly used values of the significance level, such as 0.001, 0.01, 0.05, 0.10, etc. Now, if a significance level of 0.0483 is taken, which is not at all a commonly used significance level, it would appear that the P-value obtained from the particular test must have been found to be just below 0.0483, so that the null hypothesis will definitely be rejected at the significance level of 0.0483. Alternatively, if the researcher is aiming to fail to reject the null hypothesis, then, choosing 0.0483 as the significance level would suggest that the P-value obtained from the particular test must have been found to be just above 0.0483, so that the null hypothesis will fail to be rejected at the significance level of 0.0483. Thus, choosing a significance level of a number like 0.0483 would indicate that it was chosen to specifically arrive at a conclusion as per the wish of the researcher, which would, in turn, make the results of the study unreliable to believe in.