Question

I read a claim that 40% of Americans struggle to afford at least one basic need for housing, healthcare, utilities, or food. A Math 146 student hopes this proportion is lower for Bellingham Technical College students.

1. What are the null and alternate hypotheses?

H0:     p≥.40

Ha: p≤ .40

2. The student conducts a random survey of fellow students at BTC which returns a sample proportion of 38% who cannot afford basic needs. Test the claim at the 5% significance level. State all reasoning, steps, values, and interpretations needed for the test.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.40

H_a : p < 0.40

n = 146

= 38% = 0.38

P₀ = 0.40

1 - P₀ = 1 - 0.40 = 0.60

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.38 - 0.40 / [(0.40 * 0.60) / 146]

= -0.49

Test statistic = -0.49

This is the right tailed test .

P(z < -0.49) = 0.3121

P-value = 0.3121

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the claim .