Problem 1.2.30
Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.
The top six final scores at the 2021 U.S. Women’s Figure Skating Championships are listed. (Source: NBC Sports)
232.61 215.33 214.98 213.39 199.95 178.89
Problem 1.2.4
"Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
For data at the interval level, you cannot calculate meaningful differences between data entries."
Problem 1.2.13
"Determine whether the data are qualitative or quantitative. Explain your reasoning.
Distances of track events"
Problem 1.2.19
"Determine the level of measurement of the data set. Explain your reasoning.
The top ten fiction hardcover books on The New York Times Best Sellers List based on sales in the week ending March 6, 2021, are listed. (Source: The New York Times)
1. Life After Death
2. The Four Winds
3. Klara and the Sun
4. Dark Sky
5. The Affair
6. The Midnight Library
7. The Lost Apothecary
8. The Vanishing Half
9. Infinite Country
10. A Court of Silver Flames"
Problem 1.2.32
"Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.
The numbers of performances for the 10 longest-running original runs of Broadway shows as of March 15, 2020, are listed. (Source: Playbill)
13,370 9692 9302 7485 6836 6680 6137 5959 5758 5461"
Problem 1.3.11
Determine whether the study is an observational study or an experiment. Explain.
A research study compared the memory retention of subjects when a learning activity was followed by a brief period of wakeful rest and when a learning activity was followed by a brief period of distraction. (Source: Springer Nature)
Problem 1.3.13
Determine whether the study is an observational study or an experiment. Explain.
A study used periodic blood pressure readings and brain MRIs of adults to find that adults with long periods of high blood pressure were more likely to develop cerebral small blood vessel disease. (Source: American Heart Association)
Problem 1.3.19a
A company wants to test the effectiveness of a new acne cream. The company recruits 500 girls ages 13 to 17 who have acne. The subjects are randomly assigned into two groups. One group is given the acne cream and the other is given a placebo that looks exactly like the acne cream. Both groups apply the cream daily for two months. Facial photos are taken at the beginning and end of the treatment to compare results.
Identify the experimental units and treatments used in this experiment.
Problem 1.3.19b
A company wants to test the effectiveness of a new acne cream. The company recruits 500 girls ages 13 to 17 who have acne. The subjects are randomly assigned into two groups. One group is given the acne cream and the other is given a placebo that looks exactly like the acne cream. Both groups apply the cream daily for two months. Facial photos are taken at the beginning and end of the treatment to compare results.
b. Identify a potential problem with the experimental design being used and suggest a way to improve it.
Problem 1.3.19c
A company wants to test the effectiveness of a new acne cream. The company recruits 500 girls ages 13 to 17 who have acne. The subjects are randomly assigned into two groups. One group is given the acne cream and the other is given a placebo that looks exactly like the acne cream. Both groups apply the cream daily for two months. Facial photos are taken at the beginning and end of the treatment to compare results.
c. How could this experiment be designed to be double-blind?
Problem 1.3.20a
Researchers in Japan tested the effect of cannabidiol (CBD) in treating late teenagers with social anxiety disorder (SAD). Thirty-seven 18- to 19-year-old teenagers with SAD took part in the study. The patients were assigned at random to receive a daily dose of either CBD or a placebo for 4 weeks. Symptoms were measured using The Fear of Negative Evaluation Questionnaire and the Liebowitz Social Anxiety Scale at the beginning and end of the treatment. (Source: Frontiers in Psychology)
a. Identify the experimental units and treatments used in this experiment.
Problem 1.3.24
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain.
Questioning university students as they leave a college cafeteria, a researcher asks 342 students about their eating habits.
Problem 1.3.27
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain.
Soybeans are planted on a 48-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.
Problem 1.3.29
Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain.
The average GPA of the 85 students on a college football team roster
Problem 1.3.30
Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain.
The average distance traveled to a stadium by 55,000 spectators
Problem 1.3.33
Determine whether the survey question is biased. If the question is biased, suggest a better wording.
How much do you exercise during an average week?
Problem 1.3.34
Determine whether the survey question is biased. If the question is biased, suggest a better wording.
How does the media influence the opinions of voters?
Problem 1.3.2
What is the difference between a census and a sampling?
Problem 1.3.6
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A double-blind experiment is used to increase the placebo effect.
Problem 1.3.9
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
Problem 1.3.4
What is replication in an experiment? Why is replication important?
Problem 1.3.20b
"Researchers in Japan tested the effect of cannabidiol (CBD) in treating late teenagers with social anxiety disorder (SAD). Thirty-seven 18- to 19-year-old teenagers with SAD took part in the study. The patients were assigned at random to receive a daily dose of either CBD or a placebo for 4 weeks. Symptoms were measured using The Fear of Negative Evaluation Questionnaire and the Liebowitz Social Anxiety Scale at the beginning and end of the treatment. (Source: Frontiers in Psychology)
Identify a potential problem with the experimental design being used and suggest a way to improve it."
Problem 1.3.20c
"Researchers in Japan tested the effect of cannabidiol (CBD) in treating late teenagers with social anxiety disorder (SAD). Thirty-seven 18- to 19-year-old teenagers with SAD took part in the study. The patients were assigned at random to receive a daily dose of either CBD or a placebo for 4 weeks. Symptoms were measured using The Fear of Negative Evaluation Questionnaire and the Liebowitz Social Anxiety Scale at the beginning and end of the treatment. (Source: Frontiers in Psychology)
The experiment is described as a placebo-controlled, double-blind study. Explain what this means."
Problem 1.3.20d
"Researchers in Japan tested the effect of cannabidiol (CBD) in treating late teenagers with social anxiety disorder (SAD). Thirty-seven 18- to 19-year-old teenagers with SAD took part in the study. The patients were assigned at random to receive a daily dose of either CBD or a placebo for 4 weeks. Symptoms were measured using The Fear of Negative Evaluation Questionnaire and the Liebowitz Social Anxiety Scale at the beginning and end of the treatment. (Source: Frontiers in Psychology)
How could blocking be used in designing this experiment?"
Problem 1.3.21
A researcher wants to study the effects of sleep deprivation on motor skills. Eighteen people volunteer for the experiment: Jake, Arya, Xavier, Nyla, Shaniece, Chen, Juan, Hana, Nia, Ansel, Liam, Bruno, Mei, Zoey, Kayla, Liam, Sofia, and Kai. Use a random number generator to choose nine subjects for the treatment group. The other nine subjects will go into the control group. List the subjects in each group. Tell which method you used to generate the random numbers.
Problem 1.3.22
Volunteers for an experiment are numbered from 1 to 90. The volunteers are to be randomly assigned to two different treatment groups. Use a random number generator different from the one you used in Exercise 21 to choose 45 subjects for the treatment group. The other 45 subjects will go into the control group. List the subjects, according to number, in each group. Tell which method you used to generate the random numbers.
Problem 1.3.25
"Identify the sampling technique used, and discuss potential sources of bias (if any). Explain.
After a hurricane, a disaster area is divided into 200 equal grids. Thirty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most."
Ch. 1 - Introduction to Statistics
