Sociologists studying the behavior of high school freshmen in a certain state collected data from a random sample of freshmen in the population. They constructed the 90 percent confidence interval 6.46±0.416.46±0.41 for the mean number of hours per week spent by freshmen in extracurricular activities.

Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?

For all freshmen in the state, 90 percent of the freshmen spend between 6.05 hours and 6.87 hours per week in extracurricular activities.

A. The probability is 0.90 that the mean number of hours spent in extracurricular activities for freshmen in the sample is between 6.05 hours and 6.87 hours per week.

B. The probability is 0.90 that the mean number of hours spent in extracurricular activities for freshmen in the state is between 6.05 hours and 6.87 hours per week.

C. We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the sample is between 6.05 hours and 6.87 hours per week.

D. We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the state is between 6.05 hours and 6.87 hours per week.

E

Step-by-step explanation:

A percent confident interval is usually say that we agree **%** confident that the true population mean lies in between **interval** thus making E the best answer because it follows that format and has the population (freshmen in the state) rather than the sample (freshmen in the sample)

C

Step-by-step explanation:

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Confidence interval displays the probability that a parameter will fall between a pair of values around the mean.The correct interpretation of the interval is We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the sample is between 6.05 hours and 6.87 hours per week. Hence the option c is correct option.

Given-

The 90 percent confidence interval 6.46±0.416.46±0.41 for the mean number of hours per week spent by freshmen in extracurricular activities.

90 percent of the freshmen spend between 6.05 hours and 6.87 hours per week in extracurricular activities.

Confidence interval displays the probability that a parameter will fall between a pair of values around the mean.

Thus the correct interpretation of the interval is We are 90 percent confident that the mean number of hours spent in extracurricular activities for freshmen in the sample is between 6.05 hours and 6.87 hours per week. Hence the option c is correct option.

For more about the confidence interval follow the link below-

step-by-step explanation:

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