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 280 found that 70% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?

The p-value of the test is of 0.0536 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the executive's claim.

Step-by-step explanation:

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.

At the null hypothesis, we test if the proportion is of 75%, that is:

At the alternate hypothesis, we test if the proportion is different of 75%, that is:

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

75% is tested at the null hypothesis:

This means that

A random sample of 280 found that 70% of the readers owned a particular make of car.

This means that

Value of the test statistic:

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion differing from 0.75 by at least |0.7 - 0.75| = 0.05, which is P(|z| > 1.93), which is 2 multiplied by the p-value of z = -1.93.

Looking at the z-table, z = -1.93 has a p-value of 0.0268.

2*0.0268 = 0.0536.

The p-value of the test is of 0.0536 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the executive's claim.