Question

A publisher reports that 74% of their readers own a particular make of car. A marketing executive wants to test the claim that the actual percentage is actually less than the reported percentage. A random sample of 310 found that 70% of readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim? Round p-value to four decimal places.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.74

Ha : p < 0.74

n =310

= 0.70

P0 = 0.74

1 - P0 = 1 - 0.74 =0.26

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.70 - 074 / [(0.74*0.26) / 310]

= -1.60

Test statistic = z = -1.60

P(z < -1.60 ) = 0.0548

P-value = 0.0548

= 0.052

P-value >

0.0548 > 0.02

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that