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You wish to test the following claim (H) at a significance level of a = 0.002. Ho:p=0.6 Ha:p> 0.6 You obtain a sample of size n = 176 in which there are 117 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) The p-value for this test is (assuming H, is true) the probability of observing... O at most 117 successful observations at least 117 successful observations What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value= The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to.. O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. O The sample data support the claim that the population proportion is greater than 0.6. There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.6

You wish to test the following claim (H) at a significance level of a = 0.002. Ho:p=0.6 Ha:p> 0.6 You obtain a sample of size n = 176 in which there are 117 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) The p-value for this test is (assuming H, is true) the probability of observing... O at most 117 successful observations at least 117 successful observations What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value= The p-value is... O less than (or equal to) a O greater than a This test statistic leads to a decision to.. O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. O The sample data support the claim that the population proportion is greater than 0.6. There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.6

MATLAB: An Introduction with Applications
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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**Testing a Statistical Hypothesis** **Claim to Test:** We wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.002\). - \(H_0: p = 0.6\) - \(H_a: p > 0.6\) **Sample Information:** You obtain a sample of size \(n = 176\) with 117 successful observations. For this test, use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) **P-Value Determination:** The p-value for this test is (assuming \(H_0\) is true) the probability of observing: - Option 1: at most 117 successful observations - Option 2: at least 117 successful observations **Calculating the P-Value:** What is the p-value for this sample? (Report answer accurate to four decimal places.) - P-value = [Blank] **P-Value Comparison:** The p-value is... - Option 1: less than (or equal to) \(\alpha\) - Option 2: greater than \(\alpha\) **Decision on Hypothesis:** This test statistic leads to a decision to... - Option 1: reject the null - Option 2: accept the null - Option 3: fail to reject the null **Final Conclusion:** As such, the final conclusion is that... - Option 1: There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. - Option 2: There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. - Option 3: The sample data support the claim that the population proportion is greater than 0.6. - Option 4: There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.6. This exercise demonstrates the process of hypothesis testing using the binomial distribution, emphasizing interpreting p-values and making statistical decisions based on them.
Transcribed Image Text:**Testing a Statistical Hypothesis** **Claim to Test:** We wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.002\). - \(H_0: p = 0.6\) - \(H_a: p > 0.6\) **Sample Information:** You obtain a sample of size \(n = 176\) with 117 successful observations. For this test, use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) **P-Value Determination:** The p-value for this test is (assuming \(H_0\) is true) the probability of observing: - Option 1: at most 117 successful observations - Option 2: at least 117 successful observations **Calculating the P-Value:** What is the p-value for this sample? (Report answer accurate to four decimal places.) - P-value = [Blank] **P-Value Comparison:** The p-value is... - Option 1: less than (or equal to) \(\alpha\) - Option 2: greater than \(\alpha\) **Decision on Hypothesis:** This test statistic leads to a decision to... - Option 1: reject the null - Option 2: accept the null - Option 3: fail to reject the null **Final Conclusion:** As such, the final conclusion is that... - Option 1: There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. - Option 2: There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.6. - Option 3: The sample data support the claim that the population proportion is greater than 0.6. - Option 4: There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.6. This exercise demonstrates the process of hypothesis testing using the binomial distribution, emphasizing interpreting p-values and making statistical decisions based on them.
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