We want to test whether two randomly selected polls are different (assume sample
ID: 2927286 • Letter: W
Question
We want to test whether two randomly selected polls are different (assume sample size >30). The first has a result of 41% and the second has a result of 51%. While in the field, we are told that the standard of error is 4.5% (not margin of error). Your boss, who is running for re-election, needs to know right away whether they are different (and you've left your iPad and t distribution tables at home). For your margin of error, you'll need to come up with a t-score on the fly. Based on these finding you tell your boss:
A.
The polls are not likely to be statistically different, with 95% confidence levels for each poll result of about 36.5-45.5 vs. 46.5-55.5.
B.
The polls are likely to be statistically different, with 95% confidence levels of about 36.5-45.5 vs. 46.5-55.5. You can bank on the increase.
C.
Cannot make any decision at all because the value of the t-score is not available.
D.
Cannot make any decision at all because the distribution of the population is unknown.
E.
The polls are likely to be statistically different, with 95% confidence levels for each poll result of about 32-50 vs. 42-60.
F.
The polls are not likely to be statistically different, with 95% confidence levels for each poll result of about 32-50 vs. 42-60.
G.
You cannot make any decisions at all because statistics is a difficult and confusing art.
We want to test whether two randomly selected polls are different (assume sample size >30). The first has a result of 41% and the second has a result of 51%. While in the field, we are told that the standard of error is 4.5% (not margin of error). Your boss, who is running for re-election, needs to know right away whether they are different (and you've left your iPad and t distribution tables at home). For your margin of error, you'll need to come up with a t-score on the fly. Based on these finding you tell your boss:
A.
The polls are not likely to be statistically different, with 95% confidence levels for each poll result of about 36.5-45.5 vs. 46.5-55.5.
B.
The polls are likely to be statistically different, with 95% confidence levels of about 36.5-45.5 vs. 46.5-55.5. You can bank on the increase.
C.
Cannot make any decision at all because the value of the t-score is not available.
D.
Cannot make any decision at all because the distribution of the population is unknown.
E.
The polls are likely to be statistically different, with 95% confidence levels for each poll result of about 32-50 vs. 42-60.
F.
The polls are not likely to be statistically different, with 95% confidence levels for each poll result of about 32-50 vs. 42-60.
G.
You cannot make any decisions at all because statistics is a difficult and confusing art.
Explanation / Answer
About 95% of the data lie within 2 standard deviations from the mean according to 68 95 99.7% rule.
Therefore for 95% CI, z = 2
Margin of error, M = 2*4.5 = 9%
Answer: Option F
The polls are not likely to be statistically different, with 95% confidence levels for each poll result of about 32-50 vs. 42-60.
The confidence intervals intersect and therefore the difference is not significant
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