Question

The Gallup survey company conducted a poll in May 2011. Researchers asked a random sample of about 1000 U.S. adults the following question: “From what you know or have read about raising the debt ceiling, would you want your member of Congress to vote in favor of, that is, for raising the debt ceiling, to vote against raising the debt ceiling, or do you not know enough about this issue to say?” Forty-eight percent of the adults who responded said that they would want their Congress member to vote against raising the debt ceiling. In July, 2011, the survey researchers asked a new random sample of about 1000 U.S. adults the same question. Forty-two percent of the adults who responded indicated that they would want their Congress member to vote against raising the debt ceiling. The margin of error for a 95% confidence level for the difference in the two proportions of adults who want their Congress member to vote against raising the debt ceiling was reported as 4.35%.

Supporting Details:

Alternative Hypothesis: HA: pm − pj ≠ 0.

Null Hypothesis: HO: pm − pj = 0

Part A) Imagine that there was a true difference between May, 2011 and July, 2011 in the proportion of all U.S. adults who wanted their Congress member to vote against raising the debt ceiling. Imagine also that the difference between the sample proportions was not statistically significant. Which type of error would this be?

A. Type I Error

B. Type II Error

C. Calculation error

Part 2) Sometimes researchers find that there is a statistically significant difference between sample proportions even if there is no true difference. For example, suppose there is no true difference in the proportion of all U.S. adults who wanted their Congress member to vote against raising the debt ceiling in May, 2011 and in the proportion in July, 2011. But, the difference between the sample proportions was statistically significant, this would be an instance of which of the following types of error?

A. Type I Error

B. Type II Error

C. Calculation error

Part 3) The z-statistic for the difference between the two sample proportions is equal to 2.697 with a P-value of 0.007. What conclusion could you make about the difference between the two population proportions if the level of significance is set to 0.05?

A. The difference is not statistically significant because the sample proportion difference of 0.06 is equal to the significance level of 0.05.

B. The difference is not statistically significant because the significance level of 0.05 is greater than the P-value of 0.007.

C. The difference is statistically significant because the P-value of 0.007 is less than the significance level of 0.05.

D. The difference is statistically significant because the z-statistic of 2.697 is greater than the significance level of 0.05.

Answer 1