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

Answer:

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

Step-by-step 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

     $\r p = \frac{16}{50 }$

    $\r p = 0.32$

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

      $SE = \sqrt{ \frac{0.35 (1- 0.35 )}{ \sqrt{50 } } }$

      $SE = 0.067$

So  

    The test statistics is  evaluated as

                $t = \frac{\r p - p }{ SE }$

=>             $t = \frac{0.32 - 0.35 }{ 0.067 }$

=>             $t = -0.45$

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