Question

Technology. In Exercises 9–12, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Airport Data Speeds Data Set 32 “Airport Data Speeds” in Appendix B includes Sprint data speeds (mbps). The accompanying TI-83/84 Plus display results from using those data to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results.

Short answer

The hypotheses are as follows.

$$\begin{gathered} H_0:\mu ⩾4 \\ {H}_1:\mu <4 \end{gathered}$$

The test statistic is 0.366, and the p-value is 0.3579.

The null hypothesis is failed to be rejected, and hence, there is insufficient evidence to support the claim that the population mean is less than 4 Mbps.

Step-by-step solution

Given information

A sample is taken from Airport Data Speeds to test the claim that the population mean is less than 4.00 Mbps.

State the hypotheses

The null hypothesis $H_0$represents the population greater than or equal to 4. The original claim does not contain equality. So, it becomes an alternative hypothesis $H_1$.

Thus, the test is one-tailed.

Let $\mu$be the population mean of the internet speed at the airport.

The null and alternate hypotheses are as follows.

$$\begin{gathered} H_0:\mu ⩾4 \\ {H}_1:\mu <4 \end{gathered}$$

State the test statistic and the p-value 

The test statistic and the p-value are represented by the symbols $t$and p, respectively.

State the test statistic and p-value obtained fromthe second row andthe third row of the output, respectively, as follows.

$$\begin{gathered} t=-0.3662917532 \\ \approx -0.366 \\ p=0.3578621222 \\ \approx 0.3579 \end{gathered}$$

State the decision

If the p-value is less than the significance level, the null hypothesis is rejected; otherwise, it is failed to be rejected.

Assume that the significance level is 0.05. The p-value is greater than the significance level.

Thus, the null hypothesis is failed to be rejected at a 0.05 significance level.

Conclusion 

Thus, it can be concluded that there is not sufficient evidence to support the claim that the mean data speeds for the population are lesser than 4 Mbps, at a 0.05 level of significance.