A drapery store manager was interested in determining whether a new employee can
ID: 3394709 • Letter: A
Question
A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 vertical blind installations of each of the two employees and computes the following information.
New Employee
Veteran Employee
Sample Size
10
10
Sample Mean
22.2 min
24.8 min
Standard Deviation
0.90 min
0.75 min
A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 vertical blind installations of each of the two employees and computes the following information.
New Employee
Veteran Employee
Sample Size
10
10
Sample Mean
22.2 min
24.8 min
Standard Deviation
0.90 min
0.75 min
Using the null and alternate hypothesis:
H0:mu1-mu2=0 vs. Ha:mu1-mu2<0
Calculate the value of the test statistic
New Employee
Veteran Employee
Sample Size
10
10
Sample Mean
22.2 min
24.8 min
Standard Deviation
0.90 min
0.75 min
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0
At level of significance = 0.05
As we can see, this is a left tailed test.
Calculating the means of each group,
X1 = 22.2
X2 = 24.8
Calculating the standard deviations of each group,
s1 = 0.9
s2 = 0.75
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 10
n2 = sample size of group 2 = 10
Thus, df = n1 + n2 - 2 = 18
Also, sD = 0.370472671
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -7.018061528 [ANSWER, TEST STATISTIC]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.