Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.

Airport Data Speeds: The claim that for Verizon data speeds at airports, the mean\({\bf{\mu = 14}}{\bf{.00}}\;{\bf{mbps}}\). The sample size is \({\bf{n = 13}}\) and the test statistic is

t =-1.625 .

The claim states that the mean of data speeds is\(\mu = 14.00\;{\rm{mbps}}\).

The sample size is\(n = 13\) with the test statistic \(t = - 1.625\).

As per the claim, the hypotheses are stated as follows.

\(\begin{array}{l}{H_0}:\mu = 14\;({\rm{null}}\;{\rm{hypothesis}})\\{H_1}:\mu \ne 14\;({\rm{alternative}}\;{\rm{hypothesis}}\;{\rm{and}}\;{\rm{original}}\;{\rm{claim}})\end{array}\)

Hence,it is a two-tailed test.

The degrees of freedom for the given set of data are as follows.

\(\begin{array}{c}df = n - 1\\ = 13 - 1\\ = 12\end{array}\)

The test is a two-tailed with 12 degrees of freedom and test statistic value of

-1.625.

In Table A-3, check for the value 1.625 in the row with 12 degrees of freedom to see test statistic. The value 1.625 lies between 1.356 and 1.782.

The corresponding two-tailed area indicates the P-value between 0.10 and 0.20.

Hence, this can be written as\(0.10 < \;P - value < \;0.20\)

Thus, the range of p-value is 0.10 and 0.20.