Question

A publisher reports that 74 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 70% of the readers owned a laptop. Is there sufficient evidence at the 0.05 level to support the executive's claim?

A. there is sufficient evidence to support the claim that the percentage of readers who own a laptop is different from 74%.

B.there is not enough sufficient evidence to support the claim that the percentage of readers who own a laptop is different from 74%.

Answer 1

Solution:

Given that a publisher reports that 74% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually more than the reported percentage i.e.70%

Sample size:n =300

Sample proportion P =0.70

Level of significance,=0.05

1)Null hypothesis:H0: p=0.74

Alternative hypothesis:Ha:p>0.74

Assuming H0 to be true i.e.. p = 0.74,

2)Standard error of sample proportion=p(1-p)/n=0.74(1-.74)/300=0.0253

3)Test statistics,z=P-p/Standard error=(0.70-0.74)/0.0253=-1.581

The below screenshot gives the P-value.

4)Since p-value greater than 0.05, we fail to reject null hypothesis

There is sufficient evidence to support the claim that the percentage of readers who own a laptop is different from 74%.

Option A is the correct answer.