AP Stats Chapter 10 Practice Test

Anne claims that a store-brand fertilizer works better than homemade compost as a soil enhancement when growing tomatoes. To test her theory, she plants two tomato plants in each of five planters. One plant in each planter is grown in soil with storebrand fertilizer and the other plant is grown in soil with homemade compost, with the choice of soil determined at random. In three months, she will harvest and weigh the tomatoes from each plant. What is the correct confidence interval Anne should use to analyze these data?

• The correct interval cannot be determined without the data

Answer explanation

Notice that Anne has 5 pairs of tomato plants: one in each pair is randomly assigned to each of two different soil types.

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

• 27.84

• 22.73

• 13.13

• 16.07

• 190

You want to compute a 90% confidence interval for the mean difference in height for mothers and their adult daughters using a random sample of 30 mothers who have an adult daughter. What critical value should you use for this interval? (Enter 3 decimal places)

Answer explanation

The 𝑡* value for 90% confidence and df = 29 is 𝑡* = 1.699.

We want to construct a one-sample 𝑡 interval for a population mean using data from a population with unknown shape. In which of the following circumstances would it be inappropriate to construct the interval based on an SRS of size 14 from the population?

• A boxplot shows that the values above the median are much more variable than the values below the median.

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

• The sample standard deviation is small.

• The sample standard deviation is large.

• A histogram of the data shows slight skewness.

Answer explanation

We should not use 𝑡 procedures when the sample size is small (𝑛<30) and the distribution is skewed (the values above the median are much more variable than the values below the median).

A 90% confidence interval for the mean 𝜇 of a population is computed from a random sample and is found to be 90 ± 30. Which of the following 𝑐𝑜𝑢𝑙𝑑 be the 95% confidence interval based on the same data?

• 90 ± 21

• Without knowing the sample size, any of the above answers could be the 95% confidence interval.

• 90 ± 39

• 90 ± 70

• 90 ± 30

Answer explanation

The margin of error for a confidence interval with 95% confidence will have a larger margin of error, but not more than double the margin of error for a 90% confidence interval.

Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours. For a random sample of 45 seniors without part time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours. Assuming the conditions are met, which of the following is the correct standard error for a 95% confidence interval for a difference in the population means?

• 
• 
• 
• 
• 

Answer explanation

Be careful to not confuse the means with the standard deviations in this expression.

Few people enjoy melted ice cream. Being from the sunny state of Arizona, Megan and Jenna decided to test if generic vanilla ice cream melts faster than Breyers vanilla ice cream. At 10 different times during the day and night, the girls put a single scoop of each type of ice cream in the same location outside and timed how long it took for each scoop to melt completely. When constructing a paired 𝑡 interval for a mean difference using these data, which of the following distributions should Megan and Jenna check for Normality? Select all that apply.

• The distribution of melt time for the generic ice cream.

• The distribution of difference in melt time

• The distribution of melt time for the Breyers ice cream

Answer explanation

The individual distributions do not need to be Normally distributed, but the distribution of the differences do.

A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was $57,005 with a margin of error of $742. Which of the following is the most appropriate conclusion?

• 90% of all possible samples of this same size would result in a sample median that falls within $742 of $57,005.

• 90% of the households in the sample interviewed by the Census Bureau had incomes in the interval $57,005 ± $742.

• 90% of all households had incomes in the interval $57,005 ± $742.

• The Census Bureau got the result $57,005 ± $742 using a method that will capture the true median income 90% of the time when used repeatedly.

• We can be sure that the median income for all households in the country lies in the interval $57,005 ± $742.

Answer explanation

This interval does not tell us where the population median is for sure, nor does it tell us where individual incomes are. It only provides a set of plausible values for the population median.

A quiz question gives random samples of 𝑛 = 10 observations from each of two Normally distributed populations. Tom uses a table of 𝑡 distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator’s two-sample 𝑡 interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

• Tom’s confidence interval is wider.

• Janelle made a mistake; degrees of freedom has to be a whole number.

• There is insufficient information to determine which confidence interval is wider.

• Both confidence intervals are the same width.

• Janelle’s confidence interval is wider.

Answer explanation

Because Tom's interval is less precise with smaller degrees of freedom and a larger 𝑡∗, it will be wider than one calculated using technology.

The makers of a specialty brand of bottled water claim that their “mini” bottles contain 8 ounces of water. To investigate this claim, a consumer advocate randomly selected a sample of 10 bottles and carefully measured the amount of water in each bottle. The mean volume was 7.98 ounces and the 95% confidence interval for true mean volume is 7.93 to 8.03 ounces.

Complete this statement.

Because ​​ (a)   ​ (b)   the interval, there ​​ (c)   convincing evidence that their claim is incorrect.

• 8
• is
• is not
• 0
• 7.98

Answer explanation

Because 8 is in the interval, there is not convincing evidence that their claim is incorrect.