Question

Question Set 2: Mean Exxam Score

A course coordinator is examining scores on an exam. In a representative sample of 35 students, the mean exxam score was 87.9 points with a standard deviation of 6.8 points.

A. Use Minitab Express to determine if there is evidence that the mean exxam score is different from 90 points in the population of all test takers. Use the five-step hypothesis testing procedure outlined below. Remember to include all relevant Minitab Express output and to clearly identify your test statistic and p value. Don't do any hand calculations. [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

B. Use Minitab Express to construct a 95% confidence interval for the mean exxam score in the population. Remember to include your relevant Minitab Express output and to clearly identify your final answer. Don't do any hand calculations. [15 points]

C. What minimum sample size would be necessary to construct a 95% confidence interval for the mean exxam score with a margin of error of 1 point? You will need to do hand calculations. Show all of your work. [10 points]

please use minitab express. thanks!

Answer 1

(a) The Minitab output is:

The hypothesis being tested is:

H₀: µ = 90

H_a: µ ≠ 90

The test statistic is -1.83.

The p-value is 0.076.

Since the p-value (0.076) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the mean score is different from 90 points in the population of all test takers.

(b) The 95% confidence interval for the mean score in the population is between 85.56 and 90.24.

(c) n = (1.96*6.8/1)^2 = 178

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