Fry Brothers Heating and Air Conditioning Inc. employs Larry Clark and George Mu
ID: 3220854 • Letter: F
Question
Fry Brothers Heating and Air Conditioning Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air-conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. 1. State the decision rule for .05 significance level: H_0: mu_LC = mu_GM; H_1: mu_LC notequalto GM. (Negative amounts should be entered with a minus sign. Round your answer to 2 decimal places.) Reject H_0 if z . 2. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic 3. Compute the p-value. (Round your answer to 4 decimal places.) p-value is 4. At the 0.05 significance level, is there a difference in the mean number of calls per day between the two employees? H_0. There is difference in the mean number of calls per day between the two employees.Explanation / Answer
Given,
xLC=4.77
xGM=5.02
nLC=40
nGM=50
SD(LC)=1.05
SD(GM)=1.23
significance level()=0.05
Z-value is 1.96
A.1) hence we reject H0 is Z<-1.96 or Z>+1.96
Z-statistic is given as
Z={(xLC-xGM)-(µLC-µGM)}/{sqrt(SD(LC)^2/nLC+ SD(GM)^2/nGM)}
Z=4.77-5.02/sqrt(1.05^2/40+1.23^2/50)
solving, we get
A.2) Z=-1.0397
calculated Z-value -1.0397 is within the limits of -1.96 to +1.96
we accept the null hypothesis
A.4) hence we can conclude that at 0.05% significance level there is no difference in the mean calls made per day between both employees
A.3) p-value is given as
p=xLC+xGM/nLC+nGM
p=4.77+5.02/40+50
p=0.10877
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