Question

A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.52, but given the number of people you've talked to about this same issue, you believe it is less than 0.52. The hypotheses for this test are Null Hypothesis: p ≥ 0.52, Alternative Hypothesis: p < 0.52. If you randomly sample 29 people and 17 of them believe that global warming is a serious issue, what is your test statistic and p-value?

Answer 1

Explanation:

Hello!

The article claims that the proportion of people that believes that global warming is a serious problem is 0.52 but people surveyed by the researcher believe that the proportion is less than 0.52.

Symbolically the hypotheses are:

H₀: p ≥ 0.52

H₁: p < 0.52

The statistic to test the population proportion is:

`Z= \frac{p'-p}{\sqrt{(p(1-p))/(ny) } }`≈N(0;1)

The sample proportion is p'= 17/29= 0.59

`Z_(H_0)= \frac{0.59-0.52}{\sqrt{(0.59*0.41)/(29) } } = 0.766= 0.77`

This test is one-tailed to the left and so is the p-value.

Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

So under the null hypothesis, the p-value is the probability of obtaining a Z-value ≤ 0.77:

P(Z≤0.77)= 0.779

I hope this helps!