Question

A company is criticized because only 16 of 50 in executive-level positions are women. The company argues that the representation of women among their executive ranks could be better but statistically it’s at least as high as the national average of 35%. Do an appropriate hypothesis test to determine if the company’s claim is false at a significance level of 0.1.

Answer 1

We can conclude that there is sufficient evidence to state that the companies claim is not false

Explanation:

From the question we are told that

The population proportion is
`p = 0.35`

The level of significance is
`\alpha = 0.10`

The sample size is n = 50

Generally the sample proportion is mathematically represented as

`\r p = (16)/(50 )`

`\r p = 0.32`

The null hypothesis is
`H_o : p\ge 0.35`

The alternative hypothesis is
`H_a : p< 0.35`

Generally the standard error is evaluated as

`SE = \sqrt{ (0.35 (1- 0.35 ))/( √(50 ) ) }`

`SE = 0.067`

So

The test statistics is evaluated as

`t = (\r p - p )/( SE )`

=>
`t = (0.32 - 0.35 )/( 0.067 )`

=>
`t = -0.45`

The p-value is obtained from the z-table , the values is

`P( Z < -0.45) = 0.32636`

From the calculation we see that

`p-value > \alpha` so we fail to reject the null hypothesis

Hence we can conclude that there is sufficient evidence to state that the companies claim is not false