Question

A publisher reports that 41% 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 240 found that 35% of the readers owned a particular make of car. Is there sufficient evidence at the 0.05 level to support the executive's claim?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.41

H_a : p 0.41

= 0.35

P₀ = 0.41

1 - P₀ = 1- 0.41 = 0.59

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.35- 0.41/ [0.41(1-0.41) /240 ]

= -1.890

P(z < -1.890) = 0.0588

P-value = 0.0588

= 0.05

p = 0.0588  ≥ 0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population proportion pp is different than α = 0.05 significance level.