AP Statistics Unit 6 - 7 Review

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

  $\sigma$

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

• z requires that the sample size is at most

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

You have an SRS of 23 observations from large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 98% confidence interval for the mean of the population?

• 2.177

• 2.183

• 2.326

• 2.500

• 2.508

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CCSS.HSS.IC.B.4

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 

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CCSS.HSS.IC.A.1

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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

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.” You can safely conclude that

• 95% of all Gallup Poll samples like this one give answers within + 3% of the true population value.

• the percent of the population who jog is certain to be between 15% and 21%.

• 95% of the population jog between 15% and 21% of the time.

• we can be 95% confident that the sample proportion is captured by the confidence interval.

• if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is

• 190

• 27.84

• 22.73

• 16.07

• 13.13

In preparing to construct a one-sample t-interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we NOT be safe constructing the interval based on an SRS of size 24 from the population?

• A stemplot of the data is roughly bell-shaped

• A histogram of the data shows slight skewness

• A stemplot of the data has a large outlier

• The sample standard deviation is large

• The t procedures are robust, so it is always safe

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CCSS.HSS.ID.A.3

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Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confident level?

• 550

• 600

• 650

• 700

• 750

You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is

• 1.645

• 1.699

• 1.697

• 1.96

• 2.045

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CCSS.HSS.IC.B.4

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?” He asks listeners to phone in and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who phoned in, 70 answered “Yes.” Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest
II. n is so large that both n(phat) and n(1-phat) are at least 10
III. The population is at least 10 times as large as the sample

• I only

• II only

• III only

• I and II only

• I, II and III