Question

The reported average cost per workbook at a large college is $27.50. A professor claims that the actual average cost per workbook is higher than $27.50. A sample of 44 different workbooks has an average cost of $28.90. The population standard deviation is known to be $5.00. Can the null hypothesis be rejected at alpha= 0.05?

Answer 1

We conclude that the actual average cost per workbook is higher than $27.50.

Explanation:

We are given the following in the question:

Population mean, μ = $27.50

Sample mean,
`\bar{x}` = $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

`H_(0): \mu = 27.50\text{ dollars}\\H_A: \mu > 27.50\text{ dollars}`

We use one-tailed z test to perform this hypothesis.

Formula:

`z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

Putting all the values, we have

`z_(stat) = \displaystyle(28.90 - 27.50)/((5.00)/(√(44)) ) = 1.8573`

Now,
`z_(critical) \text{ at 0.05 level of significance } = 1.64`

Since,

`z_(stat) > z_(critical)`

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.