Question

Statistics

Posted about 2 months ago

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The National Sleep Foundation recommends that teenagers aged 14 to 17 years old get at least 8 hours of sleep per night for proper health and wellness.
A statistics class at a large high school suspects that students at their school are getting less than 8 hours of sleep on average. To test their theory, they randomly sample 42 of these students and ask them how many hours of sleep they get per night. The mean from the sample is $\bar{x}=7.5$ hours.
Here's their alternative hypothesis:
$H_{\mathrm{a}}$ : The average amount of sleep students at their school get per night is...
What is an appropriate ending to their alternative hypothesis?
Choose 1 answer:
(A) ...not equal to 8 hours
(B) ...less than 8 hours.
(C) ...not equal to 7.5 hours
(D) ...less than 7.5 hours
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Answer from Sia

Posted about 2 months ago

Solution by Steps

step 1

Identify the null hypothesis ($H_0$) and the alternative hypothesis ($H_a$). The null hypothesis is typically a statement of no effect or no difference. In this case, the null hypothesis is that the average amount of sleep students get per night is 8 hours: $H_0: \mu = 8$ hours

step 2

The alternative hypothesis ($H_a$) is what the statistics class is trying to prove. They suspect that students are getting less than 8 hours of sleep on average. Therefore, the alternative hypothesis should be: $H_a: \mu < 8$ hours

Answer

B

Key Concept

Alternative Hypothesis

Explanation

The alternative hypothesis is a statement that indicates the presence of an effect or difference. In this case, the class suspects that the average sleep is less than 8 hours, so the appropriate alternative hypothesis is $H_a: \mu < 8$ hours.

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