AP Statistics - Chapter 8 Review

A researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% confidence interval, a 99% confidence interval will be…

• It would be narrower because it omits only 1% of the possible samples instead of 5%

• It would be wider because it has a higher confidence, which requires a larger margin of error.

• It would be narrower because it has a higher confidence, which requires a larger margin of error.

• It would be the same because the sample is the same.

• You can’t tell because the margin of error varies from sample to sample.

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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 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.

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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

A 90% confidence interval for p, the proportion of all high school students at a local high school who participate in after school activities was found to be (0.743, 0.896). Which of the following is correct?

• About 90% of the high school students have between 74.3% to 89.6% chance of participating in after school activities.

• There is a 90% probability that the sample proportion lies between 0.743 to 0.896.

• We are reasonably certain the true proportion of all high school students who participate in after school activities is between 74.3% to 89.6%.

• If a second sample was taken, there is a 90% chance that its confidence interval would contain 0.75.

• This confidence interval indicates than 75% of high school students participate in after school activities.

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A 90% confidence interval for p, the proportion of all high school students at a local high school who participate in after school activities was found to be (0.743, 0.896).

1. Which of the following would be true about a 95% confidence interval constructed using the same data?

I. The interval would be wider because the critical z* would be larger.

II. The interval would be narrower because the critical z* would be smaller.

III. The interval would be wider because the standard error would be larger.

• I only

• II only

• III only

• I and III only

• I and II only

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One reason for using a t distribution instead of 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 ơ.

• 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 t critical value.

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CCSS.HSS.ID.A.4

You are going to create a 95% confidence interval for a population proportion and want the margin of error to be no more than 0.05. Historical data indicate that the population proportion has remained constant at about 0.7. What is the minimum size random sample you need to construct this interval?

• 385

• 322

• 274

• 275

• 323

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What conditions are NOT necessary for a 95% t interval with a sample size of 9 to be valid?

• The sample was selected randomly from the population of interest.

• The population standard deviation is not known.

• It is reasonable to assume that the population is approximately normal.

• n*p-hat > 10 and n(1 - p-hat) > 10

• All of the above are necessary conditions.

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Assuming that the data came from a random sample from the population of interest, what other conditions must be met in order for the z interval to be an appropriate way to estimate a population proportion?

I. n ≥ 30 or the population is approximately normal.

II. The population size is at least 10 times greater than the sample size.

III. The population standard deviation is known

• I and III

• III and IV

• II and IV

• I, II and III

• All of the above conditions must be met.

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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 of the population?

• A stemplot of the data is roughly bell-shaped.

• A histogram of the data shows slight skewness.

• A boxplot of the data has a large outlier.

• The sample standard deviation is large.

• A Normal probability plot of the data is fairly linear.

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