The mean number of sick days an employee takes per year is believed to be about 10. Members of apersonnel department do not believe this figure. They randomly survey &8 employees. The number of sickdays they took for the past year are as follows: 12; 6; 15; 3; 10; 8; 8; 8. Let X= the number of sick daysthey took for the past year. Should the personnel team believe that the mean number is about 10? Conducta hypothesis test at the 5% level.What is the test statistic? (If using the z distribution round your answers to two decimal places, and ifusing the t distribution round your answers to three decimal places.)What is the p-value? (Round your answer to four decimal places.)Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the pointestimate and the lower and upper bounds of the confidence interval. (Round your answers to threedecimal places.)

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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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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: 12; 6; 15; 3; 10; 8; 8; 8. 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.
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.)
What is the p-value? (Round your answer to four decimal places.)
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.)

Expert Solution

Step 1

Let $μ$ denotes the population mean number of sick days an employee takes per year. The test is that the personnel team believe that the mean number is about 10 or not. The hypothesis is,

Null hypothesis:

$H_{0} : μ = 10$

Alternative hypothesis:

$H_{1} : μ \neq 10$

The descriptive statistics is conducted using EXCEL. The software procedure is given below:

Enter the data.
Select Data > Data Analysis >Descriptive Statistics> OK.
Enter Input Range as Days column.
Mark Labels in First Row.
Mark Summary Statistics.
Click OK.

The output using EXCEL is as follows:

From the output, the mean is 8.75, and the standard deviation is 3.6547.

The test statistic is,

$\begin{array}{rcl} t & = & \frac{\bar{x} - μ}{(\frac{s}{\sqrt{n}})} \\ = & \frac{8.75 - 10}{(\frac{3.6547}{\sqrt{8}})} \\ = & \frac{- 1.25}{1.2921} \\ = & - 0.967 \end{array}$

Thus, the test statistic is -0.967.

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