Question

An article claims the average typing speed for high school students lies between 35.6 and 44.4 words per minute (WPM) at approximate 95% confidence. Their data comes from a sample of 54 students. (Use 1 decimal place.) a. Give the value of x for the sample in the study. b. Give the value of the margin of error for the sample in this study. If you were to create many more confidence intervals from many different random samples, you would expect... c. ..all of the confidence intervals to have centers and widths. d. ..about % of the confidence intervals would not capture the you are trying to estimate.

Answer 1

a. x = 40 wpm

b. MOE = 4.4 wpm.

c. If you were to create many more confidence intervals from many different random samples, you would expect 95% all of the confidence intervals to have centers and widths that include the true mean.

d. About 5% of the confidence intervals would not capture the parameter (true mean) you are trying to estimate.

Explanation:

We have a 95% confidence interval for the mean with bounds 35.6 and 44.4.

This is estimated from a sample that, in this case, has a sample size of n=54.

The value of x, used to construct the interval, will be at the center of the interval. Then we can calculate the value of x as the average between the two bounds:

`\=x=(UL+LL)/(2)=(44.4+35.6)/(2)=(80)/(2)=40`

The margin of error is equal to the difference between x and any of the bounds:

`MOE=UL-\bar x=44.4-40=4.4`

c. If you were to create many more confidence intervals from many different random samples, you would expect 95% all of the confidence intervals to have centers and widths that include the true mean.

d. About 5% of the confidence intervals would not capture the parameter (true mean) you are trying to estimate.