3. Independent Random Samples of 500 Households Were Taken from a Large Metropolitan Area

Ch 11/12 AP FRQs Name______

AP STATS Date______Per______

2012 #3

3. Independent random samples of 500 households were taken from a large metropolitan area in the United States for the years 1950 and 2000. Histograms of the household size (number of people in a household) for the years are shown below.

(a) Compare the distributions of the household size in the metropolitan area for the years 1950 and 2000.

(b) A researcher wants to use these data to construct a confidence interval to estimate the change in mean household size in the metropolitan area from the year 1950 to the year 2000. State the conditions for using a two-sample t-procedure, and explain whether the conditions for inference are met.

2009 #5

5. For many years, the medially accepted practice of giving aid to a person experiencing a heart attack was to have the person who placed the emergency call administer chest compression (CC) plus standard mouth-to-mouth resuscitation (MMR) to the heart attack patient until the emergency response team arrived. However, some researchers believed that CC alone would be a more effective approach.

In the 1990s a study was conducted in Seattle in which 518 cases were randomly assigned to treatments: 278 to CC plus MMR and 240 to CC alone. A total of 64 patients survived the heart attack: 29 in the group receiving CC plus standard MMR, and 35 in the group receiving CC alone. A test of significance was concluded on the following hypotheses.

Ho: The survival rate for the two treatments are equal The test resulted in a

HA: The treatment that uses CC alone produces a higher survival rate. p-value of 0.0761.

(a) Interpret what this p-value measures in the context of this study.

(b) Based on this p-value and study design, what conclusion should be drawn in the context of this study? Use a significance level of α=0.05.

(c) Based on your conclusion in part (b), which type of error, Type I or Type II, could have been made? What is one potential consequence of this error?

2013 #1

1. An environmental group conducted a study to determine whether crows in a certain region were ingesting food containing unhealthy levels of lead. A biologist classified lead levels greater than 6.0 parts per million (ppm) as unhealthy. The lead levels of a random sample of 23 crows in the region were measured and recorded. The data are shown in the stemplot.

(a) What proportion of crows in the sample had lead levels that are classified by the biologist as unhealthy?

(b) The mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.1 ppm. Construct and interpret a 95 percent confidence interval for the mean level of crows in the region.

2008