Question

The Stanford-Binet IQ test has scores that are normally distributed with a mean of 100. A principal in an elementary school believes that her students have above average intelligence and wants verification of her belief. She randomly selects 20 students and checks the student files. She finds the following IQ scores for these 20 students. IQ scores: 110,132, 98, 97, 115, 145, 77, 130, 114, 128, 89, 101, 92, 85, 112, 79, 139, 102, 103, 89

a. Compute the sample mean and sample standard deviation of the IQs of the students sampled. Round to 1 decimal place.

b. Construct a 96% confidence interval for the mean IQ of students at this school. Show all steps in the computation of the error and the interval endpoints. Round to 1 decimal place.

c. Does this estimate support the principal’s belief? I.e., does it provide conclusive evidence that the mean IQ of her school’s students is above 100?

d. At a level of significance of .05, is there sufficient evidence, based on a hypothesis test, to conclude that students at this school have a mean IQ that is above the national mean? Show the hypotheses, the test statistic, and the p-value, with all supporting work. State whether or not the null is rejected. State a final conclusion, in context.

Answer 1