A manufacturer claims that a new Wi-Fi router has a range of 150 feet, allowing many customers to use their Wi-Fi throughout their homes and yards. An independent testing laboratory found that a random sample of 21 of these routers worked over an average distance of 142 feet, with a standard deviation of 12 feet. a. Construct a two – sided 95% confidence interval for the mean distance that the router works. b. Interpret this confidence interval. c. What can you say about the manufacturer’s claim?

a) The 95% confidence interval for the mean distance that the router works is between 117 feet and 167 feet.

b) We are 95% sure that the true mean distance that the router works is between 117 feet and 167 feet.

c) 150 feet is part of the confidence interval, so we can say that the manufacturer's claim is correct.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so the students t-distribution is used to solve this question.

a. Construct a two – sided 95% confidence interval for the mean distance that the router works.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 21 - 1 = 20

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 20 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.086

The margin of error is:

M = T*s = 2.086*12 = 25

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 142 - 25 = 117

The upper end of the interval is the sample mean added to M. So it is 142 + 25 = 167

The 95% confidence interval for the mean distance that the router works is between 117 feet and 167 feet.

b. Interpret this confidence interval.

We are 95% sure that the true mean distance that the router works is between 117 feet and 167 feet.

c. What can you say about the manufacturer’s claim?

150 feet is part of the confidence interval, so we can say that the manufacturer's claim is correct.

me! what did you put for this question?

step-by-step explanation: