Chapter 10 Worksheet 1 Confidence Intervals

Multiple Choice Practice

Short answer Practice:

1. The admissions director from Big CityUniversity found that (107.8, 116.2) is a 95%confidence interval for the mean IQ scores of allfreshman. Comment on whether each of the following explanations is correct.

(a) There is a 95% probability (chance) that theinterval form 107.8 to 116.2 contains

(b) There is a 95% chance that the interval contains x-bar.

(c) This interval was constructed using a method that captures the true mean in 95% of all possible samples.

(d) 95% of all possible samples will contain the interval (107.8, 116.2).

(e) The probability that the interval (107.8, 116.2) captures is either 0 or 1, but we don’t know which.

Chapter 10 Worksheet 1 Confidence Intervals

2. A Gallup Poll in November 2002 found that 52% of the people in the sample said “yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is ±3 percentage points.” (a) What is the 95% confidence interval for the percent of all adults who what to lose weight?

(b) Explain clearly to someone who knows no statistics why we can’t just say the 51% of all adults want to lose weight.

(c) Then explain clearly what “95% confidence” means?

(d) As Gallup indicates, the 3% margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “nonsampling errors”) could affect the accuracy of the 51% estimate?

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