Confidence Intervals

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants.

The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A survey of 121 subjects found that 84 have suffered the symptoms of depression in the last year. Calculate a 90% confidence interval for p.

• (0.612, 0.776)

• (0.641, 0.748)

• (0.780, 0.900)

• (0.621, 0.759)

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

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

A random sample of 100 WHS students found that 53 of them were in possession of a pencil. What is the p-hat for this sample?

• 0.53
• 0.5
• 0.47
• 1

Tags

CCSS.HSS.IC.B.4

A nutritionist found that in a sample of 80 families, 22% said they are apples at least once a week. Construct the 90% CI for the population proportion.

• (0.144, 0.296)
• (0.190, 0.250)
• (0.704, 0.856)
• (0.129, 0.311)

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

• 1.799

• 1.798

• 1.803

Tags

CCSS.HSS.IC.B.4

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

What is the point estimate?

• 75

• 105.2

• 10

• 0.90

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4