Question

Suppose the weights of tight ends in a football league are normally distributed such that σ2=1,369. A sample of 49 tight ends was randomly selected, and the weights are given below. Use Excel to calculate the 95% confidence interval for the mean weight of all tight ends in this league. Round your answers to two decimal places and use ascending order.

Answer 1

Answer:

Step-by-step explanation:Answer Explanation

Correct answers:

$\left(241.42,\ 262.14\right)$

A 95% confidence interval for μ is (x¯−zα/2σn‾√,x¯+zα/2σn‾√). Here, α=0.05, σ=37, and n=49. Use Excel to calculate the 95% confidence interval.

1. Open Excel, enter the given data in column A, and find the sample mean, x¯, using the AVERAGE function. Thus, the sample mean, rounded to two decimal places, is x¯=251.78.

2. Click on any empty cell, enter =CONFIDENCE.NORM(0.05,37,49), and press ENTER.

3. The margin of error, rounded to two decimal places, is zα/2σn‾√≈10.36. The confidence interval for the population mean has a lower limit of 251.78−10.36=241.42 and an upper limit of 251.78+10.36=262.14.

Thus, the 95% confidence interval for μ is (241.42, 262.14).