Question

You measure 35 textbooks' weights, and find they have a mean weight of 41 ounces. Assume the population standard deviation is 4.7 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places
_____ < μμ < ______

Answer 1

The 95% confidence interval for the true population mean textbook weight, given a sample mean of 41 ounces and a population standard deviation of 4.7 ounces for a sample size of 35, is between 39.44 ounces and 42.56 ounces.

Step-by-step explanation:

To construct a 95% confidence interval for the true population mean textbook weight, we use the following formula:

Confidence Interval = μ ± (Z* × (σ/√n))

Where:

• μ = sample mean = 41 ounces
• Z* = Z-score for 95% confidence level = 1.96 (from standard normal distribution tables)
• σ = population standard deviation = 4.7 ounces
• n = sample size = 35

Step-by-step calculation:

1. Calculate the standard error (σ/√n): (4.7/√35) = 0.794
2. Multiply the Z-score by the standard error: 1.96 × 0.794 = 1.55624
3. Add and subtract this value from the sample mean to find the confidence interval: 41 ± 1.55624

This results in a confidence interval of:

39.44 ounces < μ < 42.56 ounces

This confidence interval means that we are 95% confident that the true mean weight of the textbooks lies between 39.44 and 42.56 ounces.