Question

A publisher reports that 25% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually above the reported percentage. A random sample of 100 found that 30% of the readers owned a laptop. Is there sufficient evidence at the 0.10 level to support the executive's claim?

Determine the ?-value of the test statistic. Round your answer to four decimal places.

Answer 1

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

H0: p = 0.25 versus Ha: p > 0.25

This is an upper tailed test.

We are given

Level of significance = α = 0.10

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 30

n = sample size = 100

p̂ = x/n = 30/100 = 0.30

p = 0.25

q = 1 - p = 0.75

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.30 - 0.25)/sqrt(0.25*0.75/100)

Z = 1.1547

Test statistic = 1.1547

P-value = 0.1241

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the percentage is actually above the reported percentage.