AP Stats 10.2 Quiz - Estimating a Difference in Means

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 store-brand 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. Which of the following is the correct confidence interval Anne should use to analyze these data?

• Two-sample z interval for μ ₁ − μ ₂

• Paired z interval for μ _{d i f f}

• Two-sample t interval for μ ₁ − μ ₂

• Paired t interval for μ _{d i f f}

• The correct interval cannot be determined without the data

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

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?

• 
• 
• 
• 
• 

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

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’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.