Question

You measure 22 randomly selected textbooks' weights, and find they have a mean weight of 59 ounces. Assume the population is normally distributed and has a standard deviation of 4.9 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

Answer 1

To construct a 90% confidence interval for the true population mean textbook weight, we can use the following formula:

CI = X ± Zα/2 * (σ/√n)

where:

X = sample mean = 59 ounces

Zα/2 = critical value for the confidence level, α/2 = 0.05, which can be looked up in a standard normal distribution table. For a 90% confidence level, the critical value is 1.645.

σ = population standard deviation = 4.9 ounces

n = sample size = 22

Substituting the values, we get:

CI = 59 ± 1.645 * (4.9/√22)

CI = 59 ± 1.645 * 1.042

CI = 59 ± 1.713

CI = (57.29, 60.71)

Therefore, we can be 90% confident that the true population mean textbook weight is between 57.29 ounces and 60.71 ounces.