Question

Among 1501 respondents to a survey, 20% said that there is no solid evidence to support global warming. Use a 0.01 significance level to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. State the final conclusion. A. There is not sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming. B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming. C. There is sufficient evidence to support the claim. D. There is sufficient evidence to support the claim that more than 25% of the population believes that there is no solid evidence to support global warming.

Answer 1

B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.

Explanation:

The following information has been availed;

n = 1501

sample proportion = 20% = 0.2

Level of significance = 0.01 = 1%

We are required to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. In mathematical notation this claim can be written as;

p < 0.25, where p is the population proportion. From this information, we can formulate the following set of hypotheses;

H0: p ≥ 0.25

Ha: p < 0.25 (claim). This will be a left-tailed test.

The test statistic for hypothesis on population proportions is z, defined by the formula;

`z=\frac{sampleproportion-p}{\sqrt{(p(1-p))/(n) } }`

where p is the population proportion under the null hypothesis, that is p = 0.25.

Using the given information , the test statistic becomes;

`z=\frac{0.2-0.25}{\sqrt{(0.25(1-0.25))/(1501) }}=-4.4736`

The next step is to compute the p-value in our left-tailed test;

p-value = P(Z < -4.4736) = 0

Our p-value is less than the level of significance and thus we reject the null hypothesis in favor of the alternative hypothesis which is also our claim. The final conclusion is thus;

There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.