Question

Key Family Heating and Air Conditioning Inc. employs Andy Clark and Frank John to make service calls to repair furnaces and air-conditioning units in homes. A. Key, the owners would like to know whether there is a difference in the mean number of service calls they make per day.  A random sample of 40 days last year showed the following:

Days (n)	Sample Mean	Population Standard Deviation
A. Clark	40	4.77	1.05
F. John	50	5.02	1.23

At the .05 significance level, is there a difference in the mean number of calls per day between the two employees?

a. State the hypotheses

b. Determine the critical value =

c State the decision rule: Reject H_{0 if}

_d. Calculate the test statistic =

e. Make a decision:

Answer 1

We are given that

The claim is either the null hypothesis or the alternative hypothesis.The null hypothesis and the alternative hypothesis state the opposite of each other.The null hypothesis needs to include an equality.

CLARK	JOHN
4.77	5.02	MEAN
1.05	1.23	STANDARD DEVIATION
40	50	n

df	88
difference (Clark - John)	-0.25000
pooled variance	1.33102
pooled std. dev	1.15370
standard error of difference	0.24474
hypothesized difference	0
t	-1.02

p-value (two-tailed)	0.3098
confidence interval 95% lower	-0.73636
confidence interval 95% upper	0.23636
margin of error	0.48636

Ho: mL - mG = 0

Ha: mL - mG is not 0

Test statistic: t = -1.0397
p-value: 0.3014
df = 87,60
Since the p-value is greater than 5%, fail to reject Ho.
The test supports saying there is no difference.