Question

A publisher reports that 34% 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 30% 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 hypotheses are as follows:

H_{​​​​​​0} : P = 34% = 0.34 i.e.The population proportion of readers of a publisher who own a particular make of car is 0.34.

H_{​​​​​​1} : P ≠ 0.34 i.e.The population proportion of readers of a publisher who own a particular make of car is not equal to 0.34.

To test the hypothesis we shall use one z-test for single proportion. The test statistic is given as follows:

Where, p is sample proportion, P is population proportion specified under H_{​​​​​​0}, Q = 1 - P and n is sample size.

Sample proportion of the readers who owned a particular make of car is, p = 0.30

Sample size (n) = 220,

P = 0.34 and Q = 1 - 0.34 = 0.66

The value of the test statistic is -1.25245.

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows,

p-value = 2P(Z > |z|)

We have, |z| = 1.25245

p-value = 2P(Z > 1.25245)

Using "pnorm" function of R we get, P(Z > 1.25245) = 0.1052

Hence, p-value = 2 × 0.1052 = 0.2104

P-value of the test statistic is 0.2104.

Please rate the answer. Thank you.