Question

One issue that the Gallup Organization studies and surveys is Global Warming. One question that is included in their surveys is: “Do you think that global warming will pose a serious threat to you or your way of life during your lifetime? In the past, 33% of Americans surveyed answered ‘Yes’ to this question. In January 2020, 405 of the 1012 Americans surveyed answered ‘Yes’ to this same question.   Does this 2020 data provide sufficient evidence to conclude that Americans are becoming more concerned about the impact of global warming on their lifestyles?

	a.	H0: p < .40   Ha: p =.40
	b.	H0: p > .33   Ha: p ≤ .33
	c.	H0: p > .33 Ha: p ≤ .33
	d.	H0: p = .33 Ha: p >.33
	e.	H0: p = .33    Ha: p ≠ .33

Calculate the test statistic and the p-value.

	a.	z = 4.75, p-value is approximately 1.022
	b.	z = 3.24, p-value = 0.005
	c.	z = 4.75, p-value is approximately 0
	d.	z = 1.645, p-value = 0.025
	e.	z = 1.96, p-value = 0.025

At α = 0.01, what is the correct decision?

	a.	Fail to reject Ha
	b.	Reject Ha
	c.	Reject Ho in favorof Ha
	d.	Fail to Reject Ho

Interpret your conclusion within the context of the problem.

	a.	There is not sufficient evidence to conclude that Americans are becoming more concerned about global warming and its effect on their lifestyles.
	b.	There is not sufficient evidence to conclude that Americans are becoming more concerned about global warming and its effect on their lifestyles because the participants were not randomly selected.
	c.	There is not sufficient evidence to conclude that Americans are becoming more concerned about global warming and its effect on their lifestyles because the sample size is too small.
	d.	There is sufficient evidence to conclude that Americans are becoming more concerned about global warming and its effect on their lifestyles.

Answer 1

Proportion (p0) = 0.33

Total number of sample (n) = 1012

number of favourable events (X) = 405

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (1-0.9999989788854975)

P = 0.0

Since, the test is two-tail test at = 0.01

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 2.3263478740408408

The statistic value, 4.7492 is greater than the critical value 2.3263478740408408. Hence, reject the null hypothesis.

Answers

1)

d.	H0: p = .33 Ha: p >.33

2)

c.	z = 4.75, p-value is approximately 0

3)

c.	Reject Ho in favor of Ha

4)

d.	There is sufficient evidence to conclude that Americans are becoming more concerned about global warming and its effect on their lifestyles.