Question

A consulting firm had predicted that 30% of employees at a large firm would take advantage of a new company Credit Union, but management is skeptical. They felt the rate would be lower. A survey of 250 employees show that 82 of them are currently taking advantage of the Credit Union. Calculate the appropriate test statistic based on this data.

Answer 1

According to the data presented, the most convenient is to make an approximation through Z-Stadistic Proportions) For the sample size)

So things,

A)

`H_0 = p=.30`

`SE= \sqrt{(p_0(1-p_0))/(n)} = \sqrt{(0.30(1-0.30))/(250)} = 0.0289`

b) Given
`n=250` and
`x=82` so
`\hat{p} =`sample proportion
`= (x)/(n) = (82)/(250)=0.328`

`z= \frac{\hat{p}-p_0}{\sqrt{(p_0(1-p_0)))/(n)}}=(0.328-0.3)/(0.0289)=0.96`

c)

So, A z-value less than 2 or more than 2 is considered unusually small and unusually large respectively,

Then, Since z=0.96<2, the z-test stadistic is unusually small.