O 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? OA. The conditions np 25 and nq 25 are not satisfied, so a test about a population proportion using the normal approximation method cannot be used. OB. 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. OC. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method cannot be used. OD. 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? OA. This statement means that if the P-value is not very low, the null hypothesis should be rejected. O B. This statement means that if the P-value is very low, the null hypothesis should be accepted.

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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.

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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?

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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.
Transcribed Image Text: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.
Transcribed Image Text: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.
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