Question

You measure 40 textbooks' weights, and find they have a mean weight of 52 ounces. Assume the population standard deviation is 5.4 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

Answer 1

Explanation:

We want to determine a 95% confidence interval for the true population mean textbook weight.

Number of sample, n = 40

Mean, u = 52 ounces

Standard deviation, s = 5.4 ounces

For a confidence level of 95%, the corresponding z value is 1.96.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

52 ± 1.96 × 5.4/√40

= 52 ± 1.96 × 0.85

= 52 ± 1.666

The lower end of the confidence interval is 52 - 1.666 = 50.33 ounces

The upper end of the confidence interval is 52 + 1.666 = 53.67 ounces

Therefore, with 95% confidence interval, the true population mean textbook weight is between 50.33 ounces and 53.67 ounces