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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: 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) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) -Select-v= O Part () What is the p-value? O p-value < 0.010 O 0.010 < p-value <0.050 O 0.050 < p-value < 0.100 O p-value > 0.100 Explain what the p-value means for this problem. O If Ho is true, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10. O If Ho is false, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10. O If Ho is false, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10. O If Ho is true, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.

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: 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) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) -Select-v= O Part () What is the p-value? O p-value < 0.010 O 0.010 < p-value <0.050 O 0.050 < p-value < 0.100 O p-value > 0.100 Explain what the p-value means for this problem. O If Ho is true, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10. O If Ho is false, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10. O If Ho is false, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10. O If Ho is true, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.

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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note: for part E, the select options are either z or t distribution (must pick one)

The text describes a hypothesis test regarding the mean number of sick days an employee takes per year. It is stated that this mean is believed to be about 10 days. However, a personnel department doubts this number, so they conducted a survey of 8 employees. The recorded sick days for these employees in the past year are: 11, 5, 14, 3, 10, 9, 8, and 9. Let \( X \) represent the number of sick days taken by an employee. The task is to determine whether the personnel team should believe that the mean number is about 10 through a hypothesis test at the 5% significance level. Notes: - A Student's t-distribution is assumed, and the underlying population is considered to be normally distributed. The image includes several expandable sections labeled as Part (a) through Part (e) for step-by-step instructions or inputs that might be required. There is also Part (f) that specifically deals with determining the p-value and its implications. **Part (f): Determining the p-value** - What is the p-value? - Options: - \( \text{p-value} < 0.010 \) - \( 0.010 < \text{p-value} < 0.050 \) - \( 0.050 < \text{p-value} < 0.100 \) - \( \text{p-value} > 0.100 \) - Explanation of what the p-value means for the problem: - If \( H_0 \) is true, there is a chance equal to the p-value that the average number of sick days for employees is not at least as different from 10 as the sample mean. - If \( H_0 \) is false, there’s a chance equal to the p-value that the average number of sick days is at least as different from 10 as the sample mean. A text box allows for the input of the calculated test statistic, with a note to round answers to two decimal places for the z distribution and three decimal places for the t distribution.
Transcribed Image Text:The text describes a hypothesis test regarding the mean number of sick days an employee takes per year. It is stated that this mean is believed to be about 10 days. However, a personnel department doubts this number, so they conducted a survey of 8 employees. The recorded sick days for these employees in the past year are: 11, 5, 14, 3, 10, 9, 8, and 9. Let \( X \) represent the number of sick days taken by an employee. The task is to determine whether the personnel team should believe that the mean number is about 10 through a hypothesis test at the 5% significance level. Notes: - A Student's t-distribution is assumed, and the underlying population is considered to be normally distributed. The image includes several expandable sections labeled as Part (a) through Part (e) for step-by-step instructions or inputs that might be required. There is also Part (f) that specifically deals with determining the p-value and its implications. **Part (f): Determining the p-value** - What is the p-value? - Options: - \( \text{p-value} < 0.010 \) - \( 0.010 < \text{p-value} < 0.050 \) - \( 0.050 < \text{p-value} < 0.100 \) - \( \text{p-value} > 0.100 \) - Explanation of what the p-value means for the problem: - If \( H_0 \) is true, there is a chance equal to the p-value that the average number of sick days for employees is not at least as different from 10 as the sample mean. - If \( H_0 \) is false, there’s a chance equal to the p-value that the average number of sick days is at least as different from 10 as the sample mean. A text box allows for the input of the calculated test statistic, with a note to round answers to two decimal places for the z distribution and three decimal places for the t distribution.
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