Question

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; 14; 3; 11; 9; 7; 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. State the distribution to use for the test. What is the test statistic? What is the p-value? 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.) **Please use a TI*$ Plus where possible**

Answer 1

Solution: The null and alternative hypotheses are:

State the distribution to use for the test.

Answer: We need to use here t-distribution

What is the test statistic?

Answer: We can use TI-84 to find the test statistic. The steps are as follows:

Step 1: Press STAT and click on Edit

Step 2: Enter the given data in L1

Step 3: After entering all the observations, press STAT and scroll right to TESTS

Step 4: Scroll down to T: Test...

Step 5: Click on data and enter:

List: L1

Freq: 1

Click on Calculate.

The output is given below:

Therefore, the test statistic is:

rounded to three decimal places

What is the p-value?

Answer:

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.

Answer: We can use TI 84 to find the 95% confidence interval for the true mean. The steps are as follows:

Step 1: Press STAT and scroll right to TESTS

Step 2: Scroll down to TInterval... and scroll to data

Enter

List: L1

Freq: 1

C-Level : .95

Calculate

The output is given below:

Therefore, the point estimate is: