Question

The teachers union is concerned about the amount of time teachers spend each week doing schoolwork at home. A simple random sample of 56 teachers had a mean of 8.0 hours per week working at home after school. Assume that the population standard deviation is 1.5 hours per week. Construct a 95% confidence interval estimate for the mean number of hours per week a teacher spends working at home.

A. [6.35, 9.65]
B. [6.87, 9.13]
C. [7.25, 8.75]
D. [7.65, 8.35]

Answer 1

To construct a 95% confidence interval estimate for the mean number of hours per week a teacher spends working at home, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) x (Standard Deviation / √Sample Size). In this case, the sample mean is 8.0 hours, the population standard deviation is 1.5 hours, and the sample size is 56. The critical value for a 95% confidence interval is approximately ±1.96. The confidence interval for the mean number of hours per week a teacher spends working at home is [6.35, 9.65].

Step-by-step explanation:

To construct a 95% confidence interval estimate for the mean number of hours per week a teacher spends working at home, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) x (Standard Deviation / √Sample Size)

In this case, the sample mean is 8.0 hours, the population standard deviation is 1.5 hours, and the sample size is 56. The critical value for a 95% confidence interval is approximately ±1.96. Plugging these values into the formula, we get:

Confidence Interval = 8.0 ± (1.96) x (1.5 / √56)

Calculating this expression gives us a confidence interval of [6.35, 9.65]. Therefore, the correct answer is A. [6.35, 9.65].