Question

The average monthly cell phone bill was reported to be $50.07 by the U.S. Wireless Industry. Random Sampling of a large cell phone company found the following monthly cell phone charges (in dollars):52.62 46.27 59.77 67.2157.26 49.24 45.99 46.8155.39 48.08At the 0.05 level of significance, can it be concluded that the average phone bill has increased?

Answer 1

Answer:

The null and alternative hypotheses are:

$H_{0}:\mu= 50.07$

$H_{a}:\mu>50.07$

Under the null hypothesis, the test statistic is:

$t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}} }$

Where:

$\bar{x} = 52.86$ is the sample mean

$s=7.0132$ is the sample standard deviation

$n=10$ is the sample size

$\therefore t=\frac{52.86-50.07}{\frac{7.0132}{\sqrt{10}} }$    

          $=1.26$

Now, the right tailed t critical value at 0.05 significance level for df = n-1 = 10-1 = 9 is:

$t_{critical}=1.833$

Since the t statistic is less than the t critical value at 0.05 significance level, therefore,we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the average phone bill has increased.