Hypothesis Testing
Complete the following hypothesis test.

A recent study on Xaniaville University college students suggested that the mean time to complete an undergraduate degree for all students, regardless of their work schedule, was 3.5 years. Based on this study, to increase enrollment, the marketing department at Xaniaville University decided to invest $500,000 in advertising to promote to the community that if you attend Xaniaville, you will be finished in 3.5 years, or less, with your undergraduate degree.

You would like to be the future director of the marketing department after graduating. In order to create a good reputation for yourself, you decide to research the fact that the degree can be completed in 3.5 years because you have talked to all your friends and they have informed you that there is no possible way they could complete their degree in that time frame.

You chose a random sample of 233 college graduates to conduct your research. Your results revealed the mean time to complete an undergraduate degree was 3.9 years with a standard deviation of 2 years.

At the .05 significance level, can we conclude that undergraduate students can complete an undergraduate degree in a mean of 3.5 years, or less? You have taken a statistics class and know that to determine this information you can apply the five-step hypothesis testing procedure. You complete the following to present to the marketing director, George Longstocking:

Step 1. The null hypothesis and the alternate hypothesis are:

H0: P = 0.5 null hypotheses
H1 : P


Step 2. The level of significance is:

Step 3. The test statistic is:

Step 4. The decision rule is:

Step 5. The value of the test statistic and decision regarding the hypothesis are:


Your conclusion and advice to George are: (be sure to address Type I or II error, whichever applies in this case.)

George thinks you are trying to take his job so he does nothing with your advice. You decide to speak to his direct manager. What recommendations would you make to the University VP of Finance who is about to approve a $500,000 expense to move forward with the aforementioned marketing plan?