1. Which of the following statistics is defined as the 50th percentile?
(A) The mean
(B) The median
(C) The mode
(D) The interquartile range
(E) The standard deviation
2. A researcher wanted to estimate the average amount of money spent on extracurricular activities per school in a certain region. The researcher randomly selected 20 public schools and 20 private schools in the region to use for a sample. Which of the following best describes the type of sample that was taken?
(A) A census
(B) A cluster sample
(C) A convenience sample
(D) A simple random sample
(E) A stratified random sample
3. Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of z=1.72 before the conversion, what is the standardized score for the student after the conversion?
(E) The standardized score for the student after the conversion cannot be determined.
4. A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias?
(A) The wording of the questions in the survey leads people to respond in a certain way.
(B) The behavior of the interviewer leads people to respond in a certain way.
(C) People might be uncomfortable with the survey questions and, as a result, might not always respond to those questions truthfully.
(D) Many of the people selected to participate in the survey who do not respond might have opinions different from those who do respond.
(E) People without telephones are overlooked in the sampling procedure used to determine who is surveyed.
1. A university researcher is interested in comparing the percents of high school seniors who took a college entrance exam for two different regions of the country, Region I and Region II. The researcher recorded the percent of seniors taking the exam for each high school within the two regions. The boxplots of the distributions of the percents of seniors who took the college entrance exam are shown below.
(a) Compare the distributions of percents of seniors who took the college entrance exam for the two regions.
(b) In writing a report, the researcher produced a single histogram of the combined data for Region I and Region II. Describe the shape of the histogram for the combined data.
2. The weights of red delicious apples are approximately normally distributed with a mean of 9 ounces and a standard deviation of 0.75 ounce. An online gift store sells gift boxes containing 5 red delicious apples. At the time of packaging, 5 red delicious apples are randomly selected and packaged in a box.
(a) Describe the distribution of the total weight of the 5 randomly selected apples.
(b) What is the probability that the total weight of the 5 randomly selected apples will be less than 42 ounces?
(c) The combined weight of the packing material and box in which the apples will be shipped is always 10 ounces. Let W represent the weight of a complete packaged gift box, which consists of the packing material, box, and 5 randomly selected apples. What are the mean and the standard deviation of W ?
3. Recently, a company acquired the rights to use a forest—like the one shown in the photograph below—to harvest trees to produce lumber.
The company wants to conduct a study to estimate the mean trunk diameter of the trees from the forest by taking a random sample of approximately 5 percent of the trees from the forest. For the study, the company divides the forest into 200 equally sized plots of approximately one acre each, as shown in the figure below.
Because of previous logging practices and growth patterns, plots with older trees, such as Plot 6, tend to have fewer trees but with larger trunk diameters, and plots with younger trees, such as Plot 121, tend to have more trees but with smaller trunk diameters. This is illustrated in the two figures of Plots 6 and 121 by the varying number and sizes of the symbol +.
(a) Describe a procedure for using cluster sampling to obtain a random sample of approximately 5 percent of the trees from the forest, using the plots as clusters.
(b) Describe a procedure for using stratified sampling to obtain a random sample of approximately 5 percent of the trees from the forest, using the plots as strata.
(c) For the study, give one advantage of using cluster sampling as described in part (a) over stratified sampling as described in part (b).
(d) For the study, give one advantage of using stratified sampling as described in part (b) over cluster sampling as described in part (a).