Question

Fred is constructing a 95% confidence interval to estimate the average length (in minutes) of movies he watches. His random sample of 15 movies averaged 114 minutes long with a standard deviation of 11 minutes. What critical value and standard error of the mean should he use?

A) t*=2.131,SE=2.84
B) t*=2.131,SE=2.94
C) t*=2.131,SE=11
D) t*=2.145,SE=2.84
E) t*=2.145,SE=2.94

Answer 1

Fred should use a critical value of approximately 2.145 and a standard error of 2.84 to construct the 95% confidence interval for the average length of movies.

Step-by-step explanation:

Fred is constructing a 95% confidence interval to estimate the average length (in minutes) of movies he watches, with a random sample of 15 movies averaging 114 minutes and a standard deviation of 11 minutes. The critical value for a 95% confidence interval using the Student's t-distribution should be obtained from the t-distribution table using degrees of freedom (n-1) and the desired confidence level. Since the sample size is 15, the degrees of freedom would be 14. Consulting a t-table, the critical value (t*) for a 95% confidence interval with 14 degrees of freedom is approximately 2.145. To calculate the standard error of the mean (SE), we use the formula SE = s / sqrt(n), where 's' is the sample standard deviation and 'n' is the sample size. Using the provided standard deviation of 11 minutes and the sample size of 15 movies, the standard error is SE = 11 / sqrt(15) ≈ 2.84. Hence, the correct critical value and standard error should be t*=2.145 and SE=2.84.