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The true mean hours of sleep a night for college students in the United States is 6.2 hours. Suppose you want to use a hypothesis test to determine whether the mean hours of sleep a night for BYU-Idaho students is higher than the national mean.

Which of the following pairs of hypotheses is the most appropriate for addressing this question?

A. [tex]H_0: \mu = 6.2 \quad H_a: \mu > 6.2[/tex]

B. [tex]H_0: \mu > 6.2 \quad H_a: \mu = 6.2[/tex]

C. [tex]H_0: \mu = 6.2 \quad H_a: \mu \neq 6.2[/tex]

D. [tex]H_0: \mu \neq 6.2 \quad H_a: \mu = 6.2[/tex]

E. [tex]H_0: \mu = 6.2 \quad H_a: \mu < 6.2[/tex]

F. [tex]H_0: \mu < 6.2 \quad H_a: \mu = 6.2[/tex]

Answer :

Answer:

Option A)

[tex]H_{0}: \mu = 6.2\text{ hours}\\H_A: \mu > 6.2\text{ hours}[/tex]

Step-by-step explanation:

We are given he following in the question:

Population mean = 6.2 hours.

The hypothesis wants to determine if the mean hours of sleep a night of students is higher than the national mean.

Thus, we can design the null and alternate hypothesis as:

[tex]H_{0}: \mu = 6.2\text{ hours}\\H_A: \mu > 6.2\text{ hours}[/tex]

The null hypothesis states that mean hours of sleep a night of students is equal to the national mean that is 6.2 hours.

The alternate hypothesis states that mean hours of sleep a night of students is higher than the national mean that is 6.2 hours.

Thus, the correct answer is

Option A)

[tex]H_{0}: \mu = 6.2\text{ hours}\\H_A: \mu > 6.2\text{ hours}[/tex]

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Rewritten by : Barada

Final answer:

The correct hypotheses for testing if BYU-Idaho students sleep more than the national average are H0: μ = 6.2 and Ha: μ > 6.2, where H0 represents the national average and Ha suggests BYU-Idaho students sleep more.

Explanation:

The most appropriate pair of hypotheses for determining whether the mean hours of sleep a night for BYU-Idaho students is higher than the national mean (6.2 hours) is H0: μ = 6.2 and Ha: μ > 6.2. Here, H0 is the null hypothesis which states that the mean hours of sleep for BYU-Idaho students is the same as the national average, which is 6.2 hours. The alternative hypothesis, Ha, suggests that the mean hours of sleep for BYU-Idaho students are greater than the national mean. This setup aligns with the goal of the hypothesis test, which is to gather evidence that could support a claim of BYU-Idaho students sleeping more than the national average.