Question

The mean score of adult men on a psychological test that measures "masculine stereotypes" is 4.88. A researcher studying hotel managers suspects that successful managers score higher than adult men in general. A random sample of 48 managers of large hotels has mean x-bar = 5.91. Assume the population standard deviation is sigma = 3.2.

Using the null and alternative hypotheses that you set up in problem 5, the value of the test statistic for this hypothesis test is ______

Answer 1

We use z-test for this hypothesis.

`z_(stat) = 2.23`

Explanation:

We are given the following in the question:

Population mean, μ = 4.88

Sample mean,
`\bar{x}` = 5.91

Sample size, n = 48

Alpha, α = 0.05

Population standard deviation, σ = 3.2

First, we design the null and the alternate hypothesis

`H_(0): \mu = 4.88\\H_A: \mu > 4.88`

The null hypothesis states that the mean score of successful managers on a psychological test is 4.88 and the alternate hypothesis says that the mean score of successful managers on a psychological test is greater than 4.88.

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(5.91 - 4.88)/((3.2)/(√(48)) ) = 2.23`