Question

Use this information to answer Question 1 to Question 4: The management XYC Inc. wants to determine whether there is a signicant dierence in the average length of time (in minutes) employees spent on Emails every day within its two operating divisions at α = 0.05. The following data has been accumulated for this test. (The degrees of freedom associated with test statistic is given to be 59) Division 1 Division 2 Sample Mean 56.8 60.3 Sample Standard Deviation 10 18 Sample Size 51 41 1. (2 points) Write appropriate null and alternate hypothesis. 2. (2 points) Determine the critical value for this test. 3. (3 points) Calculate test statistic. 4. (2 points) Based on above information, what is your conclusion of the test?

Answer 1

1)

Null hypothesis: Ho:μ1-μ2	=	0
Alternate hypothesis: Ha: μ1-μ2	≠	0

2)

for 0.05 level ,two tail test &59 df, critical t=±

2.0010

from excel: t.inv(0.975,59)

3)

Point estimate =x1-x2=		-3.500
standard error of difference Se=√(S21/n1+S22/n2)=			3.1406
test statistic t =(x1-x2-Δo)/Se=		-1.1144

4)

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that population means differ.