In a certain​ survey, 507 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 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. 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 very​ low, the null hypothesis should be rejected. B. This statement means that if the​ P-value is very​ low, the alternative hypothesis should be rejected. C. This statement means that if the​ P-value is very​ low, the null hypothesis should be accepted. D. This statement means that if the​ P-value is not 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 alternative hypothesis has been​ rejected, but this conclusion cannot be made. B. 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. 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 high​ P-value, the alternative 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. A significance level with more than 2 decimal places has no meaning. 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. Significance levels must always end in a 1 or a 5. D. Choosing a more specific significance level will make it more difficult to reject the null hypothesis.

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6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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In a certain​ survey, 507 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 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. 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 very​ low, the null hypothesis should be rejected. B. This statement means that if the​ P-value is very​ low, the alternative hypothesis should be rejected. C. This statement means that if the​ P-value is very​ low, the null hypothesis should be accepted. D. This statement means that if the​ P-value is not 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 alternative hypothesis has been​ rejected, but this conclusion cannot be made. B. 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. 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 high​ P-value, the alternative 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. A significance level with more than 2 decimal places has no meaning. 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. Significance levels must always end in a 1 or a 5. D. Choosing a more specific significance level will make it more difficult to reject the null hypothesis.
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