Question

A publisher reports that 55% 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 200 found that 46% 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

Answer: 2.5538

Step-by-step explanation:

Claim : The proportion of readers own a particular make of car = 55 %

i.e. p=0.55

Sample size : $200$

Proportion of readers owned a particular make of car in sample  :

$P=0.46$

Now, the test statistic for the population proportion is given by :-

$z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}$

$\Rightarrow\ z=\dfrac{0.55-0.46}{\sqrt{\dfrac{0.46(1-0.46)}{200}}}\Rightarrow\ z=2.5537695922\approx2.5538$

Hence, the value of the test statistic is 2.5538