What are the null hypothesis (H,) and the alternative hypothesis (H, ) that should be used for the test? |Ho: µ is ? |H;: µ is ? ? In the context of this test, what is a Type II error? А Турe II error is ? fact, μis 2 | the hypothesis that u is ? |when, in Suppose that you decide not to reject the null hypothesis. What sort of error might you be making?

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**Hypothesis Testing in a Personality Test Subsection**

One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score, \( \mu \), among the general population on this subsection. The website reports that \( \mu \) is 142, but you believe that \( \mu \) is less than 142. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is 135 and that the standard deviation of their scores is 28.

Based on this information, answer the questions below.

---

1. **What are the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_1 \)) that should be used for the test?**

   \( H_0 \): \( \mu \) is [ Select ]  
   [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ]

   \( H_1 \): \( \mu \) is [ Select ]  
   [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ]

---

2. **In the context of this test, what is a Type II error?**

   A Type II error is [ Select ]  
   [ Options: failing to reject, rejecting ] the hypothesis that \( \mu \) is [ Select ]  
   [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ] when, in fact, \( \mu \) is [ Select ]  
   [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ].

---

3. **Suppose that you decide not to reject the null hypothesis. What sort of error might you be making?**

   [ Dropdown: Type I, Type II ] error

---
Transcribed Image Text:**Hypothesis Testing in a Personality Test Subsection** One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score, \( \mu \), among the general population on this subsection. The website reports that \( \mu \) is 142, but you believe that \( \mu \) is less than 142. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is 135 and that the standard deviation of their scores is 28. Based on this information, answer the questions below. --- 1. **What are the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_1 \)) that should be used for the test?** \( H_0 \): \( \mu \) is [ Select ] [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ] \( H_1 \): \( \mu \) is [ Select ] [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ] --- 2. **In the context of this test, what is a Type II error?** A Type II error is [ Select ] [ Options: failing to reject, rejecting ] the hypothesis that \( \mu \) is [ Select ] [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ] when, in fact, \( \mu \) is [ Select ] [ Options: less than, not equal to, greater than, equal to ] [ Input: 142 ]. --- 3. **Suppose that you decide not to reject the null hypothesis. What sort of error might you be making?** [ Dropdown: Type I, Type II ] error ---
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