A cell phone service provider has selected a random sample of 20 of its customers in an effort to estimate the mean number of minutes used per day. The results of the sample included a sample mean of 34.5 minutes and a sample standard deviation equal to 11.5 minutes. Based on this information, and using a 95 percent confidence level:
A) the critical value is z = 1.96
B) the critical value is z = 1.645
C) the critical value is t = 2.093
D) The critical value can't be determined without knowing the margin of error.

Question

Quizplus · Accepted Answer

Since the sample size is small (n = 20) and the population standard deviation is unknown, the t-distribution should be used to find the critical value for a 95% confidence interval. The degrees of freedom (df) would be n - 1 = 19, and for a 95% confidence level, the critical t-value is approximately 2.093.

A Cell Phone Service Provider Has Selected a Random Sample