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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 6.00 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.

**What are the null and alternative hypotheses?**

A) \( H_0: \mu < 6.00 \text{ Mbps} \)
\( H_1: \mu = 6.00 \text{ Mbps} \)

B) \( H_0: \mu = 6.00 \text{ Mbps} \)
\( H_1: \mu < 6.00 \text{ Mbps} \)

C) \( H_0: \mu = 6.00 \text{ Mbps} \)
\( H_1: \mu > 6.00 \text{ Mbps} \)

D) \( H_0: \mu = 6.00 \text{ Mbps} \)
\( H_1: \mu \neq 6.00 \text{ Mbps} \)

**Identify the test statistic.**
_____

**Identify the P-value.**
_____

__________ \( H_0 \). There is ___________ evidence to support the claim that the sample is from a population with a mean less than 6.00 Mbps.

Answer :

Final answer:

The correct setup for the hypothesis test, given the aim is to verify if mean data speeds are less than 6 Mbps, involves a null hypothesis (μ = 6.00 Mbps) and an alternative hypothesis (μ < 6.00 Mbps), labeled as option B. Specific values for test statistic and P-value cannot be provided without data. The decision to reject the null hypothesis depends on whether the P-value is less than the significance level of 0.05.

Explanation:

The question pertains to conducting a hypothesis test to determine if the mean data speed at airports for a specific smartphone carrier is less than 6 Mbps. When setting up hypotheses for a hypothesis test regarding a population mean, the null hypothesis (H0) is typically a statement of no effect or no difference, which assumes the status quo. In this case, it claims the mean is equal to a benchmark value (6.00 Mbps), while the alternative hypothesis (H1) represents the research question, hypothesizing the mean to be different from the benchmark value in a specific direction.

Therefore, the correct hypotheses would be:

  • H0: μ = 6.00 Mbps - The null hypothesis states that the population mean is 6.00 Mbps.
  • H1: μ < 6.00 Mbps - The alternative hypothesis claims that the population mean is less than 6.00 Mbps, aligning with the original claim that needs to be tested.

This matches option B from the given choices. Without the provided data speeds, test statistic, or P-value, I cannot give specific values for these components or make a definitive conclusion. However, the general approach would involve comparing the P-value to the significance level (α = 0.05) to decide whether to reject the null hypothesis. If the P-value is less than the significance level, there is enough evidence to reject the null hypothesis and support the alternative hypothesis claim. Otherwise, we do not have sufficient evidence to support the claim that the mean speed is less than 6.00 Mbps.

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Rewritten by : Barada