Question

A guidance counselor at a university career center is interested in studying the earning potential of certain college majors. He claims that the proportion of graduates with degrees in engineering who earn more than $75,000 in their first year of work is not 15%. If the guidance counselor chooses a 5% significance level, what is/are the critical value(s) for the hypothesis test? 2010 20.05 20.025 1.960 20.01 2.326 20.005 2.576 1.282 1.645 Use the curve below to show your answer. Select the appropriate test by dragging the blue point to a right, left- or two tailed diagram. The shaded area represents the rejection region. Then, set the critical value(s) on the z-axis by moving the slider.

Answer 1

For the critical value we know that the significance is 5% and the value for
`\alpha/2 = 0.025` so we need a critical value in the normal standard distribution that accumulates 0.025 of the area on each tail and for this case we got:

`Z_(\alpha/2)= \pm 1.96`

Since we have a two tailed test, the rejection zone would be:
`z<-1.96` or
`z>1.96`

Explanation:

Data given and notation

n represent the random sample taken

`\hat p` estimated proportion of interest

`p_o=0.15` is the value that we want to test

`\alpha=0.05` represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

`p_v` represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion of graduates with degrees in engineering who earn more than $75,000 in their first year of work is not 15%.:

Null hypothesis:
`p=0.15`

Alternative hypothesis:
`p \\eq 0.15`

When we conduct a proportion test we need to use the z statistic, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

The One-Sample Proportion Test is used to assess whether a population proportion
`\hat p` is significantly different from a hypothesized value
`p_o`.

For the critical value we know that the significance is 5% and the value for
`\alpha/2 = 0.025` so we need a critical value in the normal standard distribution that accumulates 0.025 of the area on each tail and for this case we got:

`Z_(\alpha/2)= \pm 1.96`

Since we have a two tailed test, the rejection zone would be:
`Z<-1.96` or
`z>1.96`