Question

? Among a simple random sample of 333 American adults who do not have a four-year college degree and are not currently enrolled in school, 130 said they decided not to go to college because they could not afford school. Round answers to 4 decimal places. 1. A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. What are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence supporting this statement

Answer 1

Solution:

For the given scenario, we need 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: A minority of the Americans who decide not to go to college do so because they cannot afford it.

Alternative hypothesis: H_a: A minority of the Americans who decide not to go to college do so because they cannot afford it.

H₀: p ≤ 0.5 versus H_a: p > 0.5

This is an upper tailed test.

Assume 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

x = number of items of interest = 130

n = sample size = 333

p̂ = x/n = 130/333 = 0.39039039

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.39039039 – 0.5)/sqrt(0.5*0.5/333)

Test statistic = Z = -4.0004

P-value = 1.0000

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that only a minority of the Americans who decide not to go to college do so because they cannot afford it.