C. It stays the same. 27, Not surprisingly, there is a trade-off when constructi
ID: 3066151 • Letter: C
Question
C. It stays the same. 27, Not surprisingly, there is a trade-off when constructing confidence intervals o higher confidence levels are associated with less precision d.e, wider con In the prev the interval will be vals by ha you how t tchoose one: wider, narrower). In contrast, if you desire a high degree of precis estimate, your confidence level will be(choose one: lower, h igher, in you CONFIDENCE INTERVALS FOR MEAN DIFFERENCES Scenario 4 Estima A huge employe All the confidence intervals you constructed thus far were estimating a population mean compute a confidence interval around a mean difference. For example, in a test of s larly int when th trained As a firs tion. Ea they ag Two ex students are asked to indicate how long Homo sapiens have been on Earth. Based on evidence, the best answer to that question is 200.000 years The average answer given by 50 students was 250,000 with a standard deviation of 500,000 years. Compute a 95 interval. 28. In this case, the point estimate is the difference between the sample mean and 200,000 your point estimate for the mean difference in this scenario? 29. What is the margin of error in this scenario? 30. Wh at is the upper boundary for this confidence interval? 31. What is the lower boundary for this confidence intervalt? 32. Choose the correct interpretations of this confidence interval. Select all that apply a 95% of the sample mean differences are between-92.100.1 8 and 192.100, 18. b. If multiple samples were taken from this same population, 95% of the confidence intervals would contain the population mean difference. we are 95% confident that the true value of the population mean difference is be -92,100.18 and 192,100.18. 95% of the respondents gave answers that were between-92.100.18 and 192.100 18. c, d, tweenExplanation / Answer
28.
Point estimate for the mean difference = Sample mean - 200,000
= 250,000 - 200,000
= 50,000
29.
Standard error of the mean difference = SE(Sample mean - 200,000)
= SE(Sample mean) + 0
= 500,000 / sqrt(50)
= 70710.68
Margin of error = Z value for 95% confidence interval * Standard error of the mean difference
= 1.96 * 70710.68
= 138592.93
30.
Upper boundary of the confidence interval = Point estimate + Margin of error
= 50,000 + 138592.93
= 188592.93
31.
Lower boundary of the confidence interval = Point estimate + Margin of error
= 50,000 - 138592.93
= -88592.93
32.
The correct option is,
b. If multiple samples were taken from this population, 95% of the confidence intervals would contain the population mean difference.
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