The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believé this figure. They rằndomly survéy 8 employees. The number of sick days they took for the past year are as follows: 11 5; 14; 3; 10; 9; 8; 9. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (c) O Part (d) O Part (e) O Part () O Part (g) O Part (h) O Part () Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.) 95% C.I.

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I'm having a hard time understanding how to label these boxes, so if someone could explain how to complete this correctly that would help a lot. I've been stuck on this problem for an hour now and I don't know what I'm doing wrong. Thanks

**Educational Content: Confidence Interval and Hypothesis Testing**

- **Context and Problem Statement:**
  The mean number of sick days an employee takes per year is believed to be about 10. The personnel department doubts this figure. They conduct a survey of 8 employees, gathering the number of sick days they took over the past year: 11, 5, 14, 1, 10, 9, 8, and 9 days. The question is whether the mean number is genuinely about 10. The task involves conducting a hypothesis test at the 5% significance level. For this problem, we assume the population is normally distributed, and a Student's t-distribution is used.

- **Parts to Consider:**
  - Part (a)
  - Part (b)
  - Part (c)
  - Part (d)
  - Part (e)
  - Part (f)
  - Part (g)
  - Part (h)
  - Part (i)

- **Confidence Interval and Diagram:**
  Construct a 95% confidence interval for the true mean. A graph is provided, illustrating the situation:

  - **Diagram Description:**
    The diagram is a bell-shaped curve representing the normal distribution. The central region is marked as "95% C.I.," indicating the 95% confidence interval. The bounds of this interval are noted on the horizontal axis, along with a point estimate.

  - **Important Annotations:**
    - A label for the point estimate.
    - Indications for the lower and upper bounds of the confidence interval.
  
**Instruction:**
Round your answers to three decimal places when calculating the estimates for the interval and when conducting the hypothesis test.

This exercise helps in understanding hypothesis testing and constructing confidence intervals, fundamental for inferential statistics.
Transcribed Image Text:**Educational Content: Confidence Interval and Hypothesis Testing** - **Context and Problem Statement:** The mean number of sick days an employee takes per year is believed to be about 10. The personnel department doubts this figure. They conduct a survey of 8 employees, gathering the number of sick days they took over the past year: 11, 5, 14, 1, 10, 9, 8, and 9 days. The question is whether the mean number is genuinely about 10. The task involves conducting a hypothesis test at the 5% significance level. For this problem, we assume the population is normally distributed, and a Student's t-distribution is used. - **Parts to Consider:** - Part (a) - Part (b) - Part (c) - Part (d) - Part (e) - Part (f) - Part (g) - Part (h) - Part (i) - **Confidence Interval and Diagram:** Construct a 95% confidence interval for the true mean. A graph is provided, illustrating the situation: - **Diagram Description:** The diagram is a bell-shaped curve representing the normal distribution. The central region is marked as "95% C.I.," indicating the 95% confidence interval. The bounds of this interval are noted on the horizontal axis, along with a point estimate. - **Important Annotations:** - A label for the point estimate. - Indications for the lower and upper bounds of the confidence interval. **Instruction:** Round your answers to three decimal places when calculating the estimates for the interval and when conducting the hypothesis test. This exercise helps in understanding hypothesis testing and constructing confidence intervals, fundamental for inferential statistics.
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