Question

Shortly after the Apollo 11 lunar landing on July 20, 1969 a survey revealed that 28% of Americans did not believe it had happened. You have a theory that people nowadays are just as cynical and distrustful of government as they were back then, so you randomly sample 75 people and find that 25 of them do not believe that the Apollo 11 landing actually happened. 14) Explain why the initial requirements have been met. Test the claim that the percentage is the same as its 1969 value?

Answer 1

Solution:

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

Null hypothesis: H₀: The percentage of people who believe on lunar landing of Apollo is 28%.

Alternative hypothesis: H_a: The percentage of people who believe on lunar landing of Apollo is not 28%.

H₀: p = 0.28 versus H_a: p ≠ 0.28

This is a two tailed test.

We assume level of significance = α = 0.05

We are given

x = number of items of interest = 25

n = sample size = 75

We are given n = 75, this means sample size is adequate to use z or normal distribution.

np = 75*0.28 = 21

nq = 75*0.72 = 54

np & nq > 5, so we can use normal approximation.

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

p̂ = x/n = 25/75 = 0.333333333

p = 0.28

q = 1 - p = 0.72

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.333333333 – 0.28)/sqrt(0.28*0.72/75)

Z = 1.0287

P-value = 0.3036

(by using z-table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the the percentage of people who believe on lunar landing of Apollo is 28%.

We conclude that the percentage is the same as its 1969 value.