Question

A publisher reports that 58% 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 350 found that 51% of the readers owned a particular make of car. Is there sufficient evidence at the 0.05 level to support the executive's claim?

Step 1 of 6: State the null and alternative hypotheses.

T value

p value

one tail or two tail

sufficient or not

significance level

Answer 1

Solution:

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:

Null hypothesis: H₀: The percentage of readers who own a particular make of car is 58%.

Alternative hypothesis: H_a: The percentage of readers who own a particular make of car is different from 58%.

H₀: p = 0.58 versus H_a: p ≠ 0.58

This is a two tailed test.

We are given

Level of significance = α = 0.05

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

n = sample size = 350

p̂ = 0.51

p = 0.58

q = 1 - p = 1 - 0.58 = 0.42

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.51 - 0.58)/sqrt(0.58*0.42/350)

Z = -2.6533

Test statistic = -2.6533

P-value = 0.0080

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the percentage of readers who own a particular make of car is different from 58%.

There is sufficient evidence to support the executive's claim.