Question

48% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 45% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?

Answer 1

Answer:

There is no sufficient evidence to support the executive claim

Step-by-step explanation:

From the question we are told that

     The  population proportion is  $p = 0.48$

      The  sample proportion is  $\r p = 0.45$

       The sample  size is  $n = 300$

       The  level of significance is $\alpha = 0.02$

The null hypothesis is  $H_o : p= 0.48$

The  alternative hypothesis is  $H_a : p \ne 0.48$

   Generally the test statistics is mathematically evaluated as

           $t = \frac{\r p - p }{ \sqrt{ \frac{p(1 - p )}{n} } }$

=>        $t = \frac{0.45 - 0.48 }{ \sqrt{ \frac{0.48 (1 - 0.48 )}{300} } }$

=>       $t = -1.04$

The  p-value is mathematically represented as

     $p-value = 2P(z > |-1.04|)$

Form the z-table  

                 $P(z > |-1.04|) = 0.15$

=>   $p-value = 2 * 0.15$

=>   $p-value = 0.3$

Given that  $p-value > \alpha$  we fail to reject the null hypothesis

   Hence we can conclude that there is no sufficient evidence to support the executive claim