Unit #7 Practice AP 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 a store-brand fertilizer and the other plant is grown in soil with homemade compost, with the choice of soil chosen at random.  In three months, she will harvest and weigh the tomatoes from each plant.  Which of the following is the correct confidence interval Anne should use to analyze the data?

• The correct interval cannot be determined without the data

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

• 190

• 27.84

• 22.73

• 16.07

• 13.13

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?

• 1.645

• 1.671

• 1.697

• 1.699

• 1.761

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 stemplot of the data is roughly bell-shaped

• A histogram of the data shows slight-skewness

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

• The sample standard deviation is large

• The sample standard deviation is small

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

• Without knowing the sample size, any of the above answer could be the 95% 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 population means?

• 
• 
• 
• 
• 

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?

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

II.              The distribution of melt time for the Breyers ice cream

III.            The distribution of difference in melt time

• I only

• II only

• III only

• I and II only

• I, II, and III only

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 the samples of this sample size would result in a sample median that falls within $742 of $57,005

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 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’s confidence interval is wider

• Both confidence intervals are the same width

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

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

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 the true mean volume is 7.93 to 8.03 ounces.  Based on the sample, which of the following conclusions best addresses the maker’s claim?

• Because 7.98 is in the interval, there is convincing evidence, that their claim is correct.

• Because 7.98 is in the interval, there is not convincing evidence, that their claim is incorrect.

• Because 8 is in the interval, there is convincing evidence, that their claim is correct.

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

• Because 0 is in the interval, there is convincing evidence, that their claim is incorrect.