Question

A publisher reports that 46% 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 250 found that 42% 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 :

The null and alternative hypothesis is

H0 : p = 0.46

Ha : p 0.46

= 0.42

n = 250

P0 = 0.46

1 - P0 = 1 - 0.46 = 0.54

Test statistic = z =

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

= 0.42 - 0.46/ [(0.46 * 0.54) / 250 ]

Test statistic = z = -1.27

P( z < -1.27)

= 0.1020

This is the two tailed test,

P-value = 2 * P( z < -1.27)

P-value = 2 * 0.1020

P-value = 0.2040