Sue and Javier are working on a statistics project to estimate the proportion of students at their school who have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence interval from their estimates. Consider the situation in which the sample proportion from Sue's sample is equal to the sample proportion from Javier's sample. Which of the following statements correctly describes their intervals?

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A Javier's interval will have a greater degree of confidence than Sue's interval will.
B) Sue's interval will have a greater degree of confidence than Javier's interval will.
c) The width of Sue's interval will be the same as the width of Javier's interval.
D) The width of Sue's interval will be wider than the width of Javier's interval.
E) The width of Sue's interval will be narrower than the width of Javier's interval.
Transcribed Image Text:A Javier's interval will have a greater degree of confidence than Sue's interval will. B) Sue's interval will have a greater degree of confidence than Javier's interval will. c) The width of Sue's interval will be the same as the width of Javier's interval. D) The width of Sue's interval will be wider than the width of Javier's interval. E) The width of Sue's interval will be narrower than the width of Javier's interval.
Sue and Javier are working on a statistics project to estimate the proportion of students at their school who
have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and
Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence
interval from their estimates. Consider the situation in which the sample proportion from Sue's sample is
equal to the sample proportion from Javier's sample. Which of the following statements correctly describes
their intervals?
Transcribed Image Text:Sue and Javier are working on a statistics project to estimate the proportion of students at their school who have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence interval from their estimates. Consider the situation in which the sample proportion from Sue's sample is equal to the sample proportion from Javier's sample. Which of the following statements correctly describes their intervals?
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Follow-up Question

Why did we add p+0.2056? What is the formula for finding the width? Should it not be subtraction because we have p plus and minus margin of error?

The 90% confidence interval estimate according to Sue is,
{p(1-P)
81
CI=p+1.645₁
=p±0.1828√√p(1-p)
The width of the confidence interval is,
Width = p+0.1828√√p(1− p)− p+0.1828√√p(1− p)
= 0.3656/p(1-p)
Transcribed Image Text:The 90% confidence interval estimate according to Sue is, {p(1-P) 81 CI=p+1.645₁ =p±0.1828√√p(1-p) The width of the confidence interval is, Width = p+0.1828√√p(1− p)− p+0.1828√√p(1− p) = 0.3656/p(1-p)
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Follow-up Question

How did we get the 0.1828 and 0.2056?

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