Answer:
We conclude that the actual average cost per workbook is higher than $27.50.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $27.50
Sample mean, [tex]\bar{x}[/tex] = $28.90
Sample size, n = 44
Alpha, α = 0.05
Population standard deviation, σ = $5.00
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 27.50\text{ dollars}\\H_A: \mu > 27.50\text{ dollars}[/tex]
We use one-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{28.90 - 27.50}{\frac{5.00}{\sqrt{44}} } = 1.8573[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = 1.64[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis.
Thus, we conclude that the actual average cost per workbook is higher than $27.50.
