AP Statistics Confidence Intervals for Proportions

In a survey of 104 students, it was found that 79 went to the homecoming game this year.

Calculate a 99% confidence interval for p.

• (0.652, 0.868)

• (0.691, 0.829)

• (0.678, 0.842(

• (0.685, 0.895)

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

In a survey of 104 students, it was found that 79 went to the homecoming game this year.

A 99% confidence interval for p is (0.652, 0.868). Interpret this interval.

• 99% of the time the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• The probability that the population proportion of people who went to the homecoming game this year is between 65.2% and 86.6% is 95%.

• Based on this sample, I am 99% confident that the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• 99% of all possible intervals calculated this way will capture the true proportion of people who went to the homecoming game this year

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A preliminary study suggests that 17% of people agree on an issue. How large must your sample size be so you could be within ± 5% with 95% confidence?

• 217

• 30

• 2

• 152

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A preliminary study suggests that 87% of people agree on an issue. How large must your sample size be so you could be within ± 3% of p calculate at 90% confidence?

• 7

• 466

• 5

• 338

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

You have no preliminary study to work from. How large must your sample size be so you could be within ± 3% of p at 90% confidence?

• 748

• 1068

• 11

• 1495

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

Find the critical value, z*, for 91% confidence.

• 1.70

• 1.34

• 0.18

• -1.34

Tags

CCSS.HSS.ID.A.4

Find the critical value, z* for 97%

• 1.88

• 2.17

• -1.88

• -2.17

Tags

CCSS.HSS.ID.A.4

Which confidence would result in a wider interval (assuming nothing else changed), 91% or 97%?

• 97%, z* is larger for higher confidence intervals

• 97%, the standard error is larger for higher confidence intervals

• 91%, z* is larger for lower confidence intervals

• 91%, the standard error is smaller for lower confidence intervals

Tags

CCSS.HSS.ID.A.4

For a sample, the 95% confidence interval is (0.202, 0.482).

What is the point estimate, p̂, of this sample?

• 0.28

• 0.14

• 0.342

• 0.684

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

For a sample, the 95% confidence interval is (0.202, 0.482).

What is the margin of error of this sample?

• 0.28

• 0.14

• 0.342

• 0.684

Tags

CCSS.HSS.IC.B.4