Question

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

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 test.

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