Question

2. Along with exam scores, the instructor also collected data concerning employment status of the sample of 45 World Campus students. In that sample of 45 students, 32 students reported they were employed full-time.

A. Use Minitab Express to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time. If assumptions were met, use the normal approximation method. Remember to include all relevant Minitab Express output and to clearly identify your answer. [15 points]

B. What sample size would be necessary to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time with a margin of error of 3%? You will need to do hand calculations. Show all of your work. [10 points]

C. We want to know if there is evidence that in the population of all World Campus students, more than 50% are employed full-time. Use the five-step hypothesis testing procedure to address this research question. The only hand calculations that you will need to do will be in step 1 to check assumptions; use Minitab Express for steps 2 and 3. Remember to include all relevant Minitab Express output and to clearly identify your test statistic and p value. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null

Step 5: State a “real world” conclusion

Answer 1

A) Given : n = 45 and x = 32, = 0.7111 . = 0.2889

As n* = 32 and n* = 13 both are greater than 10, so condition for normal approximation met.

We can use Minitab to find the 95% confidence interval

Go to Stat menu ---> Basic statistic ----> 1 proportion.

Select Summarized data , uncheck the hypothesis test box, then click on Option and select the options as shown below :

Click on OK

So 95% confidence interval is ( 0.578684 , 0.843538 )

B) Sample size (n) =

For 95% confidence level z = 1.96

n

n = 877

C) Claim : The population of all World Campus students more than 50% are employed full-time

Step 1) H₀ : P = 0.5 vs H_a : P > 0.5

As n*P =22.5 and n*q =22.5 both are greater than 10 , the assumption for normal approximation is satisfied.

Step 2) test statistic z = 2.83

Step 3) p value = 0.005

Step 4) As p value is less than α = 0.05 , we reject the null hypothesis

step 5) There is significant evidence that the population of all World Campus students more than 50% are employed full-time