Question

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 of (6.73, 7.67). b. 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. c. 95% of the students in the survey reported sleeping between 6.73 and 7.67 hours per day. d. 95% of the students in this high school sleep between 6.73 and 7.67 hours per day. e. a student selected at random from this population sleeps between 6.73 and 7.67 hours per day for 95% of the time.

Explanation:

• Option A: Different samples will have different confidence intervals, so it's not true that about 95% of samples will result in this exact interval (6.73, 7.67).
• Option B: The definition of a 95% confidence interval is that if we take many random samples of the same size from the population, about 95% of those samples' confidence intervals will contain the true population mean. This matches the concept.
• Option C: The confidence interval is about the population mean, not the percentage of students in the survey with that sleep time.
• Option D: It's about the population mean, not 95% of the students' individual sleep times.
• Option E: The confidence interval doesn't tell us about an individual student's sleep time over time.

Answer:

B. 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.