A random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours of sleep per day of (6.73, 7.67). Which of the following statements best summarizes the meaning of this confidence interval?
A . About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.
B. 95% of the students in the survey reported sleeping between 6.73 and 7.67 hours per day.
C. 95% of the students in this high school sleep between 6.73 and 7.67 hours per day.
D. A student selected at random from this population sleeps between 6.73 and 7.67 hours per day for 95% of the time.

Question

04-03-2021
Mathematics

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A random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours of sleep per day of (6.73, 7.67). Which of the following statements best summarizes the meaning of this confidence interval?
A . About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.
B. 95% of the students in the survey reported sleeping between 6.73 and 7.67 hours per day.
C. 95% of the students in this high school sleep between 6.73 and 7.67 hours per day.
D. A student selected at random from this population sleeps between 6.73 and 7.67 hours per day for 95% of the time.

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joaobezerra joaobezerra · Answer 1 · 2021-03-05T01:37:29+01:00

Answer:

A . About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

95% CI from a sample of 50 students is (6.73, 7.67).

This means that we are 95% sure that the population mean is in this interval, that is, about 95% samples of 50 would contain the population mean, which is given by option A.

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-03-08T07:12:06+01:00

By using basic definition of confidence interval we can say that option A " About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day." is correct.

What is confidence interval ?

confidence interval tells us the degree of certainty or uncertainty that is existent in a sampling method. It gives us a range of values, telling us we are fairly sure that our true value or parameter lies within the range.

Here given that 95% confidence interval from a sample of 50 students is (6.73,7.67). so we can say that there are 95% chance that the population mean is in this interval (6.73,7.67) , that is, about 95% samples of 50 would contain the population mean, so option A is correct

By using basic definition of confidence interval we can say that option A " About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day." is correct.

To learn more about confidence interval visit :

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