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A drapery store manager was interested in determining whether a new employee can install vertical blinds...

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Basic Math

A drapery store manager was interested in determining whether anew employee can install vertical blinds faster than an employeewho has been with the company for two years. The manager takesindependent samples of 10 vertical blind installations of each ofthe 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) State the appropriate null and alternative hypotheses to testwhether the new employee installs vertical blinds faster, on theaverage, than the veteran employee.

b) Calculate the pooled estimate of the common variance

c) Calculate the value of the test statistic

d) Set up the appropriate rejection region for the hypotheses inquestion i) assuming a = 0.05.

e) What is the appropriate conclusion?

Answer & Explanation Solved by verified expert
3.8 Ratings (517 Votes)

a)

let new and veteren employees are populaiton 1 and 2,

null hypothesis: ?1-?2 = 0
Alternate Hypothesis: ?1-?2 < 0

b)

new employee veteran employee
x1                     = 22.2000 x2                     = 24.8000
s1                     = 0.9000 s2                    = 0.7500
n1                    = 10.0000 n2                    = 10.0000
pool. var S2p= ((n1-1)s21+(n2-1)*s22)/(n1+n2-2)= 0.6863

c)

Point estimate : x1-x2                                     = -2.6000
std error of difference=Se= Sp*?(1/n1+1/n2) = 0.3705
test stat t = (x1-x2-?o)/Se = -7.02

d)

for 0.05 level with right tailed test and n-1= 18 degree of freedom, critical value of t= 1.734
Decision rule :                   reject Ho if test statistic t<-1.734

e)

as test statitic is less than crtiical value we reject null hypothesis

we have sufficient evidence to conclude that new employee installs vertical blinds faster,on the average, than the veteran employee.
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