Question

A counselor at a large high school wants to estimate the mean amount of sleep μ that students got the previous night. She selects a random sample of 10 students and asks them to record the number of hours they slept last night. Based on this sample, the 95% confidence interval for the population mean amount of sleep for all students at the high school is (5.39, 7.81) hours. (a) Interpret the confidence interval. (b) What is the point estimate that was used to create the interval? What is the margin of error? (c) It is recommended that high school students get 8 hours or more of sleep each night. Based on this survey, the students claim that, on average, students at this high school are not getting the recommended amount of sleep. Use the confidence interval to evaluate this claim.

Answer 1

According to the given confidence interval, we have that:

a) It means that we are 95% sure that the population mean amount of sleep for all students at the high school is between 5.39 and 7.81 hours.

b) The point estimate is of 6.6 hours, with a margin of error of 1.21 hours.

c) Since the entire confidence interval is below 8 hours, it is found that there is enough evidence to conclude that the students at this high school are not getting the recommended amount of sleep.

What is the interpretation of a x% confidence interval?

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

Additionally, from an interval (a,b), we have that:

• The point estimate is $\frac{a + b}{2}$.

• The margin of error is of $\frac{b - a}{2}$.

Item a:

It means that we are 95% sure that the population mean amount of sleep for all students at the high school is between 5.39 and 7.81 hours.

Item b:

The point estimate is:

$\frac{5.39 + 7.81}{2} = 6.6$

The margin of error is:

$\frac{7.81 - 5.39}{2} = 1.21$

The point estimate is of 6.6 hours, with a margin of error of 1.21 hours.

Item c:

Since the entire confidence interval is below 8 hours, it is found that there is enough evidence to conclude that the students at this high school are not getting the recommended amount of sleep.

More can be learned about confidence intervals at brainly.com/question/25779324