In a certain survey, 500 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 53% 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 sample observations are not a random sample, 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 approximation 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.- **D.** 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. 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 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 accepted. ### Understanding Misleading Memory Tricks in Hypothesis Testing**c. Misleading Memory Trick:**A commonly cited memory trick in statistics is: "If the P is high, the null will fly." This implies that a high P-value means the null hypothesis is supported. It’s crucial to understand why this can be misleading:- **A.** The statement suggests that with a high P-value, the alternative hypothesis has been rejected. However, this conclusion cannot be made solely based on a high P-value. - **B.** It suggests that with a low P-value, the null hypothesis has been proven or supported. This is incorrect, as hypothesis testing does not prove hypotheses.- **C.** It implies that with a high P-value, the null hypothesis has been proven or supported, which is misleading because hypothesis testing only fails to reject the null, not prove it.- **D.** It indicates that a high P-value suggests the alternative hypothesis has been proven or supported, which also cannot be concluded.**d. Choosing a Significance Level:**Common significance levels are 0.01 and 0.05. Using an unusual level like 0.0483 might be problematic:- **A.** Picking such a specific level can imply it was chosen to obtain a desired outcome. - **B.** There's no rule that significance levels must end in 1 or 5.- **C.** However, a significance level with more than two decimal places can be seen as arbitrary.- **D.** A very specific level could complicate the rejection of the null hypothesis.Understanding these nuances ensures proper application of statistical tests and correct interpretation of their results.

a. In USA Today survey, out of 500 people who responded, 53% said yes to replace passwords with biometric security. Requirements: The sample observations are collected randomly from the population. The sample size must be at most 5% of the population size. The quantities np and n (1 – p) must be at least 10 each. Voluntary response sample: The voluntary response sample is the sample in which the respondents by themselves participate in the study. It is also termed as self-selected sample. Justification: In this survey, the respondents have themselves participated based on their own interest. This implies that the respondents voluntarily have decided to respond in the survey and the sample is voluntary response sample. Thus, the sample is not a simple random sample and the first requirement is not satisfied. Since, a requirement is not satisfied, the methods in the section cannot be used. Correct answer: Option (A). The sample observations are not a random sample. so, a test about a population proportion using the normal approximating method cannot be used.b. Decision criteria for the P-value method: If P-value≤α, then reject the null hypothesis(H0) If P-value>α, then fail to reject the null hypothesis(H0) If P-value is low and is less than the level of significance, then the null hypothesis is rejected based on the decision criteria. Thus, the meaning of the statement “if P-value is low the null must go” is null hypothesis is rejected. Correct answer: Option (B). This statement means that if the P-value is very low, the null hypothesis should be rejected.c. In a hypothesis testing problem, there are two possible conclusions- “Reject the null hypothesis” or “Fail to reject the null hypothesis”. Note that there is a fine difference between “fail to reject” and “accept”. When we say “accept”, it means that we were searching for evidence to accept it, and the study has provided with the evidence to accept it. On the other hand, when we say “fail to reject”, it means that we were searching for evidence to reject it, and the study has not provided with the evidence to reject it. Now, by definition, the null hypothesis is constructed in such a way that the researcher wishes to nullify it, that is, the researcher tries to find evidence against it. Hence, in a hypothesis testing problem, we do not look for evidence to accept the null hypothesis, but rather, to reject it. This implies that when the study does not provide evidence against the null hypothesis, we “fail to reject it”, and do not accept it. Now, when the P-value is high, then by the decision rule, the null hypothesis would not be rejected, because the P-value would be higher than most of the possible values of α. If the given statement is used, it indicates that we “accept” the null, which is not the correct conclusion. Correct answer: Option (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. It is appropriate to choose a specific significance level such as 5% or 10% to reach the conclusions. The significance level 0.0483 is not specific, therefore, it is unwise to use this for testing a claim. Hence, the common significance levels 0.01 and 0.05 are used. Correct answer: Option (A). Choosing this specific of a significance level could give the impression that the significance level was chosen specifically to reach the desired conclusion.

Math

Statistics

In a certain survey, 500 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 53% 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? O A. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method cannot be used. O 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. OC. 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. O D. The conditions np 25 and nq 2 5 are not satisfied, so a test about a population proportion using the normal approximation method cannot be used.

In a certain survey, 500 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 53% 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? O A. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method cannot be used. O 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. OC. 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. O D. The conditions np 25 and nq 2 5 are not satisfied, so a test about a population proportion using the normal approximation method cannot be used.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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