Question

Termine a confidence interval there were 324 adults surveyed. among the participants, the mean number of hours of sleep each night was 7.5 and the standard deviation was 1.6. the margin of error, assuming a 95% confidence level, is approximately 0.17 . round to the nearest hundredth the confidence interval is to .

Answer 1

The 95% confidence interval for the average number of hours of sleep amongst the surveyed adults is between 7.33 and 7.67 hours.

Step-by-step explanation:

To determine the 95% confidence interval for the mean number of hours of sleep among 324 adults surveyed, with a mean of 7.5 hours of sleep, a standard deviation of 1.6 hours, and a given margin of error of approximately 0.17, we use the formula for a confidence interval which is: mean ± margin of error. Here, the margin of error is provided; thus, we do not need to calculate it using the standard error and the z-score for the 95% confidence level. The confidence interval is thus calculated as follows: 7.5 ± 0.17.

This results in a lower bound of 7.33 hours of sleep and an upper bound of 7.67 hours of sleep, rounding to the nearest hundredth as requested. Therefore, we are 95% confident that the true mean number of hours of sleep for the population from which the sample was drawn lies between 7.33 and 7.67 hours.