Question

A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company Credit Union, but management is skeptical. They doubt the rate is that high. A survey of 300 employees shows that 138 of them are currently taking advantage of the Credit union. From the sample proportion,

a. Find the standard deviation of the sample proportion based on the null hypothesis

b. Find the z statistic

c. Does the z statistic seem like a particularly large or small value?

Answer 1

a) 0.4770

b) 3.9945

c) z-statistics seem a large value

Explanation:

a. Find the standard deviation of the sample proportion based on the null hypothesis

Based on the null hypothesis:

`p_(0)`: 0.35

and the standard deviation σ =
`\sqrt{p_(0) *(1-p_(0)) }` =
`√(0.35 *0.65 )` ≈0.4770

b. Find the z statistic

z-statistic is calculated as follows:

z=
`(X-p_(o) )/((s)/(√(N) ) )` where

• X is the proportion of employees in the survey who take advantage of the Credit Union (
  `(138)/(300)=0.46`)
• 
  `p_(0)` is the proportion in null hypothesis (0.35)
• s is the standard deviation (0.4770)
• N is the sample size (300)

putting the numbers in the formula:

z=
`\frac{0.46-0.35} }{(0.4770)/(√(300) ) }` = 3.9945

c. Does the z statistic seem like a particularly large or small value?

z-statistics seem a large value, which will cause us to reject the null hypothesis.