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Technology. In Exercises 9鈥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 鈥淎irport Data Speeds鈥 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

Expert verified

The hypotheses are as follows.

H0:4H1:<4

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

01

Given information

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

02

State the hypotheses

The null hypothesis H0represents the population greater than or equal to 4. The original claim does not contain equality. So, it becomes an alternative hypothesis H1.

Thus, the test is one-tailed.

Let be the population mean of the internet speed at the airport.

The null and alternate hypotheses are as follows.

H0:4H1:<4

03

State the test statistic and the p-value 

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

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

t=-0.3662917532-0.366p=0.35786212220.3579

04

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.

05

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.

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