Question

A publisher reports that 75% 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 310 found that 70%

of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution:

Let p be the population proportion.

Claim to be tested is " p = 75% vs p 75% "

n = 310

Let   be the sample proportion.

= 70% = .70

Use = 0.01

Null and alternative hypothesis are

H0 : p = 0.75

H1 : p   0.75

2)The test statistic z is

z =   

=  (0.70- 0.75)/[0.75*(1 - 0.75)/310]

= -2.03

p value

sign in H1 indicates that the test is "Two Tailed"

p value =  P(Z < -2.03) + P(Z > +2.03)

= 0.0212+ 0.0212

= 0.0424

p value = 0.0424