Question

A publisher reports that 55% 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 280 found that 51% of the readers owned a laptop. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.

Answer 1

We fail to reject the null hypothesis, we accept H₀

Explanation:

Population proportion p₀ = 55 % p₀ = 0,55

Sample size n = 280

Sample mean p = 51 % p = 0,51 q = 0,49

n*p and n*q are both bigger than 10 therefore we can approximate the binomial distribution to a normal distribution

Test Hypothesis

Null Hypothesis H₀ p = p₀

Alternative Hypothesis Hₐ p ≠ p₀

Significance level is α = 0,05 but we have a two-tail test then

α/2 = 0,025

z(c) = - 1,96

Computing z(s)

z(s) = ( p - p₀ ) / √(p*q)/n

z(s) = ( 0,51 - 0,55 ) / √(0,51*0,49)/280

z(s) = - 0,04 * 16,73 / 0,5

z(s) = - 1,34

Comparing

z(s) and z(c)

- 1,34 < - 1,96

| z(s) | < | z(c)|

Then z(s) is in the acceptance region, we accept H₀