Question

A publisher reports that 80% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 74% of the readers owned a laptop. State the null and alternative hypotheses.

Answer 1

Answer:

The hypothesis is:

H₀: p = 0.80 vs. Hₐ: p ≠ 0.80.

Step-by-step explanation:

The claim made by the reporter is that 80% of the readers of his newspaper owns laptops.

The hypothesis to test this claim can be defined as:

H₀: The population proportion of the readers of this newspaper owns laptops is 0.80, i.e. p = 0.80.

Hₐ: The population proportion of the readers of this newspaper owns laptops is different from 0.80, i.e. p ≠ 0.80.

A z-test for single proportion can be used to draw conclusion about this test.

The information provided is:

The sample size is, n = 300.

The sample proportion is, $\hat p$ = 0.74.

The test statistic can be computed using the formula:

$z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}$

The decision rule of the test will be:

If the p-value of the test is less than the significance level, α then the null hypothesis will be rejected. And if the p-value is more than the significance level then the null hypothesis will be accepted.