- Describe your research question, and explain its importance.

Using a t-test, I plan to test the claim by the STAT2060 course coordinator in the University that **the mean score of the STAT2060’s final exam in the Fall 2013 was 65** (The mean score of this course in the previous years was 65). This issue is important since many students were concerned about that they had written a final exam that was more difficult than the one for last year. The populations of my interests are exam scores for all students who had written the STAT2060 final exam in the Fall 2013.

- Identify the dependent and independent variables of the question you chose

The independent variable in this research is the students in the University who wrote the STAT2060 final exam in the Fall 2013. The dependent variable is the STAT2060 final exam score of a student in this university.

- Describe how you would use the four-step hypothesis test process to answer your research question.

In order to answer my research question: **the mean score of the STAT2060’s final exam in the Fall 2013 was 65, **I randomly selected the exam scores of 16 students from instructors’ grade books. The results are listed below:

56, 67, 68, 75, 45, 80, 60, 70, 68, 58, 90, 64, 67, 77, 40, 95

**Step 1: State the null and alternative hypothesis. **

H0: M = 65

Ha: M ≠ 65

**Step 2: n=16 **

To calculate the sample mean and sample standard deviation using the above sample data, I plugged these values into the formula in stat-disk analysis. Hence; the standard deviation is s= 14.43607, rounded to 14.44 while the Sample mean = 67.5

**Step 3:** We use the above sample size of n= 16, the mean score claimed by the course coordinator = 65, the significance level of 0.05, the sample standard deviation s= 14.44 and the sample mean = 59.3, and plugging these values into the formula found in stat-disk analysis. The results are shown below.

Claim: µ = µ(hyp)

t Test

Test Statistic, t: 0.6925

Critical t: ±2.1315

P-Value: 0.4992

95% Confidence interval:

59.80546 < µ < 75.19454

Fail to Reject the Null Hypothesis

Sample does not provide enough evidence to reject the claim

**Step 4:** Since the p-value of 0.4992 is greater than the chosen significance level of 0.05, I fail to reject the null hypothesis . the claim by the course coordinator in the University that **the mean score of the STAT2060’s final exam in the Fall 2013 was 65** is correct and supported. Equivalently, the 95% confidence interval shows that we are 95% confident that the population mean (the mean exam score of all students who wrote the STAT2060 final exam) lies between 59.80546 and 75.19454.

- Explain how using a
*t*test could help you answer your research question.

The above results showed that we are 95% confident that the population mean (the mean exam score of all students who wrote the STAT2060 final exam) lies between 59.80546 and 75.19454. Since the value 65 is in the 95% confidence interval, we fail to reject the null hypothesis. So, we are 95% confident that the mean score of the STAT2060’s final exam in the Fall 2013 was 65. So, the claim by the course coordinator is correct. This proves that the exam for the Fall 2013 was the same difficulty level as the ones in the previous tears.