Question

a sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a standard deviation of 2.12 hours. construct a 98% confidence interval for the average amount of sleep students at this university got last night. provide an interpretation of your interval in the context of this data situation. we are 98% sure that the mean amount of sleep students at this university got last night is between 6.44 and hours. (write your answers in ascending order.)

Answer 1

To construct a 98% confidence interval for the average amount of sleep students at this university got last night, use the formula: Confidence Interval = sample mean ± (critical value * standard deviation/square root of sample size). In this context, we can be 98% sure that the mean amount of sleep students at this university got last night falls between 6.44 and 7.26 hours.

Step-by-step explanation:

To construct a 98% confidence interval for the average amount of sleep students at this university got last night, we can use the formula: Confidence Interval = sample mean ± (critical value * standard deviation/square root of sample size).

First, we need to find the critical value for a 98% confidence level. Since the sample size is large (148), we can use the Z-score table. The critical value for a 98% confidence level is approximately 2.33.

Plugging in the values into the formula, we get: Confidence Interval = 6.85 ± (2.33 * 2.12/square root of 148). Simplifying the expression, we get the confidence interval of (6.44, 7.26).

In this context, it means that we can be 98% sure that the mean amount of sleep students at this university got last night is between 6.44 and 7.26 hours.