Question

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports 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. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Answer 1

Answer:

The null hypothesis was failed to be rejected.

Step-by-step explanation:

The complete question is:

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports 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. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. The summary statistics are n=93​, x overbar=3.92​, s=0.51.

Solution:

The hypothesis is:

H₀: The smartphone​ carrier's mean data speed at airports is not less than 4.00 Mbps, i.e. μ ≥ 4.00.

Hₐ: The smartphone​ carrier's mean data speed at airports is less than 4.00 Mbps, i.e. μ < 4.00.

Compute the test statistic as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}\\\\=\frac{3.92-4.00}{0.51/\sqrt{93}}\\\\=-1.51$

Compute the p-value as follows:

$p-value=P(t_{n-1}$

*Use a t-table.

*If the desired degrees of freedom is not provided use the next higher value.

The p-value = 0.066 > α = 0.05

The null hypothesis was failed to be rejected.

Thus, it can be concluded that the smartphone​ carrier's mean data speed at airports is not less than 4.00 Mbps.