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.

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

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

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- Here in the option 1 wee don't know the shape by hence this option does not give the correct statement.

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-same probability is given in this option as option but both option are incorrect for the given conditions.

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-In the given problem the 90 percent confidence interval is given. Thus the freshman can say with confidence interval of 90 percent to be sample between 6.05 to 6.87 hours per week.

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.

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