Question

A random sample of 16 graduates of a certain secretarial school typed an average of 85 words per minute with a standard deviation of 8 words per minute. Assume that the number of words typed per minute of a randomly selected graduates follows a normal distribution .
1. Construct a 95% confidence interval to estimate the average number of words typed by all graduates of this school. Remember to state the assumptions and interpret the result. Following R commands may be helpful.
qnorm(.9) = 1.28

qnorm(.95) = 1.65

qnorm(.975) = 1.96

qt(0.9, df=15) = 1.34

qt(0.95, df=15) = 1.75

qt(0.975, df=15) = 2.13

2. Based on the interval from Problem 1, is it plausible that population mean typing speed of students in this secretarial school is 80 words per minute? Explain.

3. Suppose you want to conduct another survey to estimate the average number of words typed by all graduate students of this school. This time, you wish to be 90% confident that estimate of the true mean is off by less than 2 words. How large a sample is required? R commands in Problem 1 may be helpful. Use the standard deviation given in Problem 1 as an estimate of σ.

4. Which of the following would cause the confidence interval for µ in Problem 1 to become narrower? Consider each statement separately. (circle all that apply; no explanations needed.)
(a) The sample mean x decreases; everything else remains the same. (b) The sample standard deviation s decreases; everything else remains the same. (c) The sample size n increases; everything else remains the same. (d) The confidence level increases from 95% to 99%; everything else remains the same.

Answer 1

R code and explanation are given below