Question

A publisher reports that 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? Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places

Answer 1

Solution :

Given that,

= 0.48

1 - = 0.52

n = 300

Point estimate = sample proportion = = 0.45

This a two tailed test.

Ho: p = 0.48

Ha: p 0.48

Test statistics

z = ( - ) / *(1-) / n

= ( 0.45 - 0.48) / (0.48*0.52) / 300

= -1.04

P-value = P(Z < z)

= 2* P(Z < -1.04)

= 2*0.1492

= 0.2984

The p-value is p = 0.2984, and since p = 0.2984 > 0.02, it is concluded that the null hypothesis is fails to reject.

Conclusion:

It is concluded that the null hypothesis is fails to reject. Therefore, there is not sufficient evidence to claim that  the percentage

is actually different from the reported percentage 48%. at 0.02 significance level.