Question

Please help with the following, and please provide the 'R' code! Thank you! A student researcher believes that the average number of typo’s produced by Pro- fessor Who Ha per lecture is less than 28. After picking a statistical test, the student analyzed 50 lectures and recorded the number of typos as Xi for i = 1, 2, . . . , 50. The random sample yields X ̄ = 25.9 and s = 5.6.

a) Pick a test and carefully follow the 7 steps in the procedure to make your decision using α = 0.05. You may assume normality of the data, but σ is unknown. Make sure and plot out (by hand is fine) the rejection region for both the test statistic, and the non-standardized scale.

b) Plot the power curve for rejecting H0: μ ≥ 28 at α = 0.05 by computing the power P(μR) for μR = 22, 23, 24, 25, 26, 27.

Answer 1

a)

rejection region

n <- 50
df <- n-1
s <- 5.6
xbar <- 25.9

mu <- 28
t = qt(0.05 , df)
rejectValue <- mu - t * s/sqrt(n)
rejectValue

> rejectValue

26.67224

we reject if

t < -1.676551

or

Xbar <

26.67224

b)

mu <- 22:27
power <- pt( (rejectValue -mu) /(s/sqrt(n)) , df)
power

plot(mu,power)

power
[1] 0.9999998 0.9999867 0.9992727 0.9800743 0.7999482 0.3403912