The Personnel Department of a large company would like to determine the amount o

Question

The Personnel Department of a large company would like to determine the amount of time it takes for employees to arrive at work. A random sample of 12 employees is selected and the time in minutes it takes to arrive at work is recorded with the following results.

15 30 50 60 25 65 45 90 75 50 50 20

a) Calculate the sample mean x
b) Calculate an unbiased estimate for the standard deviation for the amount of time it takes for employees to arrive at work
c) Test at the 1% level of significance that the average travel time of the employees is less than 60 minutes
d) What assumption is necessary to preform this test

Note: Please calculate in Steps. I will be very greatfull.

Explanation / Answer

a)

sample mean, Xbar

sum(Xi)/n

47.91666667 AVERAGE(A2:A13)

b)

unbiased estimate for the standard deviation

s = sqrt{ sum(Xi-Xbar)^2/(n-1) }

=SQRT(5672.917/11)

22.70946339

c)

ho: average travel time of the employees is equal to 60 minutes

h1: average travel time of the employees is less than 60 minutes

t= (Mean-u)/(sd/sqrt(n))

=(47.91667-60)/(22.70946/SQRT(11))

-1.764721479

p-value

P(T<t)

=T.DIST(-1.76472,11,TRUE)

0.05266062

with t=-1.76, p>0.01, I reject ho and conclude that

average travel time of the employees is less than 60 minutes

d)

popn should be normally distributed

sample should be random

Xi (Xi-Xbar)^2 15 1083.507 30 321.007 50 4.340 60 146.007 25 525.174 65 291.840 45 8.507 90 1771.007 75 733.507 50 4.340 50 4.340 20 779.340 sum 575 5672.917 sum/n 47.91667 sum/(n-1) 515.719697

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