Question

A business school claims that students who complete a 3-month typing course can type a mean of more than 1200 words an hour. A random sample of 25 students who completed this course typed a mean of 1125 words an hour, with a standard deviation of 85 words. Assume that typing speeds for all students who complete this course have an approximately normal distribution. A) Using the P-Value method and a significance level of 1%, is there evidence to support the business school’s claim? B) Construct the corresponding confidence interval and explain how it supports your conclusion in (a).

Answer 1

Part a

H₀: µ = 1200 versus H_a: µ > 1200

We are given α = 0.01, n = 25, Xbar = 1125, S = 85, df = n – 1 = 24

Test statistic = t = (Xbar - µ)/[S/sqrt(n)]

t = (1125 – 1200) / [85/sqrt(25)]

t = -4.4118

P-value = 0.9999

P-value > α = 0.01

(by using t-table)

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that students who complete a 3-month typing course can type a mean of more than 1200 words an hour.

Part b

Confidence interval = Xbar ± t*S/sqrt(n)

t = 2.7969 (by using t-table)

Confidence interval = 1125 ± 2.7969*85/sqrt(25)

Confidence interval = 1125 ± 2.7969* 17

Confidence interval = 1125 ± 47.5480

Lower limit = 1125 - 47.5480 = 1077.45

Upper limit = 1125 + 47.5480 = 1172.55

The claim value of 1200 is not contain in above interval, so we cannot conclude that students who complete a 3-month typing course can type a mean of more than 1200 words an hour.