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.

What are the null and alternate hypotheses?

The student conducts a random survey of 56 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.

Should we accept or reject the null hypothesis? State the conclusion of this study with respect to the claim in clear simple language.

Answer 1

Given : sample size=n=56

Sample proportion=p=0.38

Significance level=0.05

Hypothesis : VS

The test statistic under Ho is,

Critical value :

Decision : Here ,

Therefore , fail to reject the null hypothesis at 5% significance level.

Conclusion : Hence , there is not sufficient evidence to conclude that this proportion is lower for Bellingham Technical College students.