The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 5; 13; 5; 9; 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 (f) O Part (g) O Part (h) O Part (i) 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.
The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 5; 13; 5; 9; 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 (f) O Part (g) O Part (h) O Part (i) 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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Author:Amos Gilat
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I need help labeling this graph. I tried putting "10" in the middle of the graph but it says it's incorrect. the lower end I think is 6.311 and the upper is 10.689.

Transcribed Image Text:**Hypothesis Testing and Confidence Intervals: Sick Days Study**
**Background:**
The mean number of sick days an employee takes per year is believed to be about 10. However, members of a personnel department doubt this figure. They conducted a survey of 8 employees, with the number of sick days reported as follows: 10, 5, 13, 5, 9, 9, 8, 9. We let \( X \) represent the number of sick days taken in the past year. The question posed is whether the personnel team should accept the mean number as approximately 10, based on a hypothesis test at the 5% significance level.
**Note:**
If using a Student's t-distribution for analysis, it is assumed that the underlying population is normally distributed. This assumption generally requires validation.
**Parts of the Analysis:**
- Part (a) through Part (i): Details are hidden behind expandable sections, indicating subsections of the problem or step-by-step instructions and calculations.
**Graphical Representation:**
The task includes constructing a 95% confidence interval for the true mean.
**Graph:**
A bell-shaped curve demonstrates the typical distribution curve for the data with a shaded area in the middle, labeled "95% C.I." This represents the confidence interval. The image indicates that the point estimate (likely the sample mean) and the lower and upper bounds of the confidence interval should be clearly marked on the graph.
Analysts are instructed to round their answers for the confidence interval to three decimal places and label the point estimate and bounds appropriately on the graph.
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