## Related questions with answers

Fry Brothers Heating andAir 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. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?

Solution

VerifiedGiven:

$\begin{align*} n_1&=\text{Sample size}=40 \\ n_2&=\text{Sample size}=50 \\ \overline{x}_1=&\text{Sample mean}=4.77 \\ \overline{x}_2=&\text{Sample mean}=5.02 \\ \sigma_1&=\text{Population standard deviation}=1.05 \\ \sigma_2&=\text{Population standard deviation}=1.23 \\ \alpha&=\text{Significance level}=0.05 \end{align*}$

Given claim: Difference in the means

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.

$\begin{align*}H_0&:\mu_1= \mu_2 \\ H_a&: \mu_1 \neq \mu_2 \end{align*}$

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