AP Statistics Confidence Interval

One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

• z can be used only for large samples

• z requires that you know the population standard deviation

• z requires that you can regard your data as an SRS from the population

• z requires that the sample size is at most 10% of the population size

• a z critical value will lead to a wider interval than a t critical value

The 90% interval for a statistics test was given by 72 +- 7. What is the lower bound for the interval?

• 7

• 72

• 65

• 79

A study found that in a sample of 44 subjects, 9 of them 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%.

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size

• decreasing the confidence level, decreasing the sample size

• increasing the confidence level, decreasing the sample size

• decreasing the confidence level, increasing the sample size.

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures

• Pythagorean Theorem

• t procedures

• np > 10 and n(1-p) > 10

Margin of error equals:

• Critical Value ∗ standard Error

• z*

• 1.96

• Standard Error

When creating a confidence interval for the difference of 2 proportions, we pool the samples when finding standard error

• True

• False

What do we use to estimate unknown parameters?

• Hypothesis Test

• Confidence Interval

• Trig Identity

• Guess and check

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content σ ?

• 90% confidence; n = 25 

• 90% confidence; n = 50 

• 95% confidence; n =25 

• 95% confidence; n =50 

• n=100 at any confidence level 

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 25 laboratory rats. A 95% confidence interval for the mean blood cholesterol level μ is 80.2 to 89.8. Which of the following would cause the most worry about the validity of this interval?

• There is a clear outlier in the data

• A stemplot of the data shows a mild right skew

• You do not know the population standard deviation σ

• The population distribution is not exactly Normal.

• None of these are a problem when using t-interval