Practice Problems for Exam 1

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?

6. Which statistic is not resistant to an outlier in the data? A. Lower quartile B. Upper quartile C. Median D. Mean 7. Which one of these statistics is unaffected by outliers? A. Interquartile range B. Mean C. Standard deviation D. Range 8. Which one of the following statistics would be affected by an outlier? A. Median B. Standard deviation C. Lower quartile D. Upper quartile Normal Distribution Practice Problems: 1. Head circumferences of adults have a normal distribution with a mean of 56 centimeters and a standard deviation of 2 centimeters. (a) Explain whether it would be unusual for an adult to have a 52-centimeter head circumference. (b) Explain whether it would be unusual for an adult to have a 62-centimeter head circumference. 2. For a bell-shaped dataset with a large number of values, approximately what z -score would correspond to a data value equaling each of the following? (a) The median. (b) The lowest value. (c) The highest value. (d) The mean.

3. Which of the following would indicate that a dataset is not bell-shaped? A. The range is equal to 5 standard deviations. B. The range is larger than the interquartile range. C. The mean is much smaller than the median. D. There are no outliers. 4. The average rainfall during the month of November in San Francisco, California, is 2.62 inches. The standard deviation is 2.79 inches. What is the standardized score ( z -score) for 5.18 inches, the rainfall in San Francisco during November 2001? 5. Weights ( X ) of adult orangutans have a normal distribution with mean 180 pounds and standard deviation 20 pounds. Find each of the following probabilities: (a) P ( X < 200 ) (b) P ( X < 165 ) (c) P ( X > 165 ) 6. Find the value z ¿ that satisfies each of the following probabilities for a standard normal random variable Z . (a) P ( Z < z ¿ ) = .025 (b) P ( Z < z ¿ ) = .975 7. The time taken for a computer to boot up, X , follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the z -score for a boot-up time of x =30 seconds? A. - 2.0 B. 0.0 C. 1.0 D. 2.0

Sampling Distribution of the Sample Mean Practice Problems: 1. Gentoo penguins are a species of penguin found near Palmer Station, Antarctica. The average bill length of all Gentoo penguins is 44mm with a standard deviation of 5mm. Suppose we take a random sample of 25 Gentoo penguins and measure their bill lengths and record the average bill length for the sample ( x ¿ . Then we repeat this process many times (that is, we take more random samples of 25 Gentoo penguins and record the average bill length for the sample each time). (a) What is the mean (average) of the sample means for all possible samples of size 25 (i.e., the mean of the sampling distribution of x )? (b) What is the standard deviation of the sample means for all possible samples of size 25 (i.e., the standard deviation of the sampling distribution of x )? (c) If we took repeated samples of size 100 would this lead to a larger or smaller standard deviation of the sample means as compared to taking repeated samples of size 25? In other words, if we sampled 100 penguins at a time instead of 25 would we expect more or less variation in the sample means?