Question

A publisher reports that 62% 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 220 found that 56% of the readers owned a particular make of car. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

SOLUTION:

From given data,

A publisher reports that 62% 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 220 found that 56% of the readers owned a particular make of car.

p = 62% = 62/100 = 0.62

The null and alternative hypotheses are

: p = 0.62  

versus

: p 0.62  

n = 220

x = (220/100)*56 = 123.2

The sample proportion is

= x/n = 123.2/220 = 0.56

Find the value of the test statistic. Round your answer to two decimal places.

The formula for calculating the test statistic is given by,

z = ( - p) / sqrt (p(1-p)/n)

z = (0.56 - 0.62) / sqrt (0.62(1-0.62)/220)

z =-1.83

The test statistic = z = -1.83 (Round your answer to two decimal places)