Hypothesis testing with one sample and correlation and regression

  1. A hat company states that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15 and a standard deviation of

0.27. At a = 0.05, can you reject the company’s claim that the mean hat size for a male is at least 7.25? Assume the population is normally distributed.

For the exercises below use the data in the table, which shows the average annual salaries (both in thousands of dollars) for public school principals and

public school classroom teachers in the United States for 11 years. (Adapted from Educational Research Service)

  1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation?


  1. Calculate the correlation coefficient r. What can you conclude?

Sample Solution