Question

25. A 2012 Gallup poll asked a random sample of 120 American adults whether they thought the news media exaggerate the seriousness of global warming. The proportion who responded "No" was 59.2%. Is this good evidence that majority of American adults do not believe the news media exaggerate the seriousness of the global warning? a) Set up appropriate null and alternative hypothesis to answer the above question b) Calculate the value of the test statistic. c) Is the data significant at the 5% level (alpha = 0.05)? Explain why or why not. d) State your conclusion in the context of the question above.

Answer 1

a) H₀: P < 0.5

H₁: P > 0.5

b) The test statistic is

P-P P(1-P)

0.592 -0.5 *0.5(1-0.5) 120

= 2.02

c) P-value = P(Z > 2.02)

= 1 - P(Z < 2.02)

= 1 - 0.9783 = 0.0217

Since the p-value is less than the significance level (0.0217 < 0.05), so we should reject the null hypothesis.

So, the data is significant at the 5% level of significance.

d) At 0.05 significance level, there is sufficient evidence to conclude that the majority of American adults do not believe the news media exaggerate the seriousness of the global warning.