Practice Problems for Exam 1

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Extra Practice Problems Identifying Population, Sample, Variable, and Individual Practice Problems: 1. A sociologist assembles a dataset consisting of the population, median household income, area measured in square miles, and number of fast-food restaurants for each of the 50 states in the United States. (a) How many variables are in this dataset? (b) What is an individual in this dataset? (c) What is the population for this dataset? (d) True or False. This is a census. 2. For each of the following variables, indicate whether the variable is categorical or quantitative. If the variable is categorical, state whether the variable is nominal or ordinal. (a) Importance of a consistent bedtime to respondent (very, somewhat, or not very important). (b) Hours of sleep last night (in hours). (c) Weights of orangutans, measured in pounds. (d) Favorite color for a car. Sampling Practice Problems: 1. A class consists of 30 students and the instructor wants to take a simple random sample of 5 students from this class. The students are labeled 1 to 30 for the selection process. Which of the following possible samples of size n = 5 is most likely to be selected? A. 11, 18, 10, 8, 25. B. 5, 10, 15, 20, 25. C. 1, 2, 3, 4, 5. D. None of the above, as they are all equally likely samples. 2. A class consists of 30 students and the instructor wants to take a simple random sample of 5 students from this class. The students are labeled 1 to 30 for the selection process. Using your calculator randomly select 5 students. Use a SEED of 12 .
Design of Experiments Practice Problems: 1. A local fruit farmer uses a crop duster to aerial spray pesticide on his 9 orchards. Each orchard is sprayed with a different pesticide (each pesticide is randomly assigned to one of the nine orchards). Each orchard contains the same 4 types of apple trees. The number of sellable apples produced per tree in each orchard is counted throughout the harvest season. (a) What is the response variable in this experiment? (b) List the two factors in this experiment and the number of levels each factor has. (c) What is the observational unit in this experiment? (d) What is the experimental unit in this experiment? 2. The current recommended daily allowance for vitamin E is 30 milligrams a day. An experiment was conducted to assess the effect of vitamin E supplements on the immune system for seniors. There were 88 subjects age 65 and older who were each randomly assigned to receive either 30 milligrams, 60 milligrams, 200 milligrams, or 800 milligrams of vitamin E for 235 days. Researchers found 200 milligrams a day of vitamin E to be the optimal dose. The 200 milligram group showed a 65% increase in response to a skin test that measures immune reaction, called delayed-type hypersensitivity response, compared with those on the 30 milligram dose. Taking 800 milligrams showed no significant improvement as compared to taking 200 milligrams. (a) Give the response variable in this experiment: (b) For this experiment, give the factor and list the levels of the factor variable: (c) List the possible treatments for this experiment: (d) What is an observational unit in this experiment? (e) What is an experimental unit in this experiment?
Numerical and Graphical Summaries Practice Problems: 1. An insurance agent is interested in the amount of money paid out in claims involving fire damage. A sample of 10 claims was selected and the amount of fire damage for each claim is listed as follows in thousands of dollars: 58 51 62 27 30 69 13 41 75 36. Use your calculator to compute the sample standard deviation of the claim amounts. 2. For each of the following two sets of data, explain which one is likely to have a larger standard deviation. (a) Set 1: Heights of the children in a kindergarten class. Set 2: Heights of all of the children in an elementary school. (b) Set 1: Systolic blood pressure for a single individual taken daily for 30 days. Set 2: Systolic blood pressure for 30 people who visit a health clinic in 1 day. 3. A set of eight systolic blood pressures is: 110, 123, 132, 150, 127, 118, 102, 122. (a) Find the median value for the dataset. (b) Find the values of the lower and upper quartiles. (c) Find the value of the interquartile range (IQR). 4. A question in the 2002 General Social Survey (GSS) conducted by the national Opinion Research Center asked participants how long they spend on e-mail each week. A summary of responses (hours) for 1881 respondents follows. (a) Explain how the summary statistics show us that at least 25% of the respondents said that they did not use e-mail. (b) What is the interval that contains the lower 50% of the responses? (c) What is the interval that contains the upper 50% of the responses? (d) Compare the mean to the median. What does this imply about the shape of the distribution? 5. Which of the following would indicate that a dataset is skewed to the right? A. The interquartile range is larger than the range. B. The range is larger than the interquartile range. C. The mean is much larger than the median. D. The mean is much smaller than the median.
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