The mean length of long-distance telephone calls placed with a particular phone company was known to be 7.8 min under an old rate structure. In an attempt to be more competitive with other long-distance carriers, the phone company lowered long-distance rates, thinking that its customers would be encouraged to make longer calls and thus that there would not be a big loss in revenue. Let μ denote the true mean length of long-distance calls after the rate reduction. What hypotheses should the phone company test to determine whether the mean length of long-distance calls increased with the lower rates?

H0: μ = 7.8

Ha: μ > 7.8

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

Let μ represent the true mean length of long-distance calls after the rate reduction

The null hypothesis is that true mean length of long-distance calls after the rate reduction is the same and equal to 7.8 minutes

H0: μ = 7.8

The alternative hypothesis is that the true mean length of long-distance calls after the rate reduction have increased that is greater than 7.8 minutes

Ha: μ > 7.8