167k views
1 vote
You measure 22 textbooks' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 5.1 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

You measure 22 textbooks' weights, and find they have a mean weight of 64 ounces. Assume-example-1

1 Answer

4 votes

Answer:

Explanation:

We want to determine a 90% confidence interval for the true population mean textbook weight.

Number of sample, n = 22

Mean, u = 64 ounces

Standard deviation, s = 5.1 ounces

For a confidence level of 90%, the corresponding z value is 1.645. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z ×standard deviation/√n

It becomes

64 ± 1.645 × 5.1/√22

= 64 ± 1.645 × 1.087

= 64 ± 1.788

The lower end of the confidence interval is 64 - 1.788 = 62.21 ounces

The upper end of the confidence interval is 64 + 1.788 = 65.79 ounces

Therefore, with 90% confidence interval, the true population mean textbook weight is between 62.21 ounces and 65.79 ounces

User Gabethegrape
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.