A random sample of 36 seventh grade students in Harvard are given an exam on a reading test. Below are their raw scores.

Question

73, 77, 80, 80, 84, 86, 91, 93, 93, 93, 94, 97, 100, 100, 103, 103, 104, 105, 105, 106, 108, 110, 111, 117. 120, 120, 123, 124, 126, 128, 129, 129, 130, 130, 136

Sample mean = 105.97

Sample standard deviation = 17.18

Nationally 30% of the students score 110 points or higher on this exam.

Q1. Construct a 90% confidence interval for the population mean.

Q2. Is the population proportion of Harvard students who score 110 points or higher different from the nationwide population proportion of students who score 110 points or higher? Construct a hypothesis test using significance level 0.05.

Q3. Suppose the national average score is 100. Is there significant difference between the Harvard average score and the national average score? Use alpha = 0.05.

Q4. Find the p-value of the test conducted in Q3.

Answer 1

It would be helpful if you tell how you are solving these problems in your class - statistical calculator, computer software, or tables. I would also like to see what work you have done on this problem. Here are some ideas for each questions.

1) Since you are using a sample standard deviation, you would use a t statistic in this problem. I do this with a TI-83 or 84 calculator. You press the STAT key, highlight and select TESTS and then you would use number

8: TInterval. Make sure STATS is highlighted and enter the required information (all given in the problem). Then select calculate at the bottom to get the answer.

2) This is a hypothesis test for one proportion. The null Hypothesis is p = 0.30. The alternate hypothesis is p not= 0.30 (the word "different" means not equal). On a TI-83 you would use 5: 1-prop z test.

3) and 4) This is a hypothesis test for one mean. The null hypothesis is mu = 100. The alternative hypothesis is mu not= 100. Select #2: t test on thee Stat Tests menu to solve the problem.

You may submit your work on this for someone to check the steps and answers. If your class does not use calculators, submit the problem again and tell what method you use in class to do the computations.