HW1_chapters_1_2_4

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University of Minnesota-Twin Cities *

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Feb 20, 2024

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PROBLEM 1 : The U.S. Department of Energy conducts weekly surveys of approximately 900 gasoline stations to determine the average price per gallon of regular gasoline in the U.S. On December 29, 2003, the average price was $1.478 per gallon. a. Identify the population. b. Identify the sample. c. Identify the parameter. d. What is the statistic? e. If the 900 gasoline stations were randomly selected from the gasoline stations in Minnesota. Is this a good sample? Explain a. The population is gasoline station. b. The sample is 900 gasoline stations. c. The parameter is the average price per gallon of regular gasoline in the U.S. d. The statistic is $1.478 per gallon (the average price on December 29, 2003) e. It is not a good sample as the range of statistic is too small compared to all states in U.S.

PROBLEM 2: Identify each of the following variables as continuous, discrete, or categorical. a. Number of sequoia trees in a randomly selected acre of Yosemite National Park b. Internet connection speed in kilobytes per second. c. Number on a football player’s jersey d. Air pressure in pounds per square inch in an automobile tire a. Discrete. b. Continuous. c. Discrete. d. Continuous.

PROBLEM 3: For each of the following variables, indicate whether you would expect its histogram to be symmetric, skewed to the right, or skewed to the left. Explain why. a) The distribution of the number of goals scored in a tough soccer game where less than 2 goals is expected. b) The distribution of the weights of a medium-sized Gala apple. a) The distribution of the age of deaths. b) The distribution of the number of people per household in an area from the U.S. where the birth rate is high. a. Skewed to the right; because the game is tough, and the score will not be high. b. Symmetric, because the sample is medium-sized Gala apple. c. Skewed to the right; because the most possible death age is old people. d. Skewed to the right; because the sample is number of people per household where the birth rate is high, which means most household has many people.

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PROBLEM 4: SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114. Give an example of an unusual SAT score. Use the general rule of standard deviation (three-standard deviation rule from the course lecture notes page 30) to justify your answer. 515+2*114=743 515-2*114=287 So, the unusual score is higher than 743, or lower than 287.

PROBLEM 5: Seventh-grade students are randomly divided into two groups. One group is taught math using traditional techniques; the other is taught math using a reform method. After a year, each group is given an achievement test to compare proficiency. a) Identify the explanatory variable and the response variable. b) Determine whether the study depicts an observational study or an experiment. c) What is another explanatory variable that we would expect to be associated with the response variable? Explain how such a variable is dealt with by the randomized nature of the experiment. a. Explanatory variable: methods of teaching. Response variable: the outcome of the achievement test. b. The study depicts an experiment, because there is independent variable controlled by experimenter to get a result of dependent variable. c. It might be the gender as human brain’s rate of maturity has difference between male and female at the age of teenagers. The randomization avoids the impact of this explanatory variable in the experiment.

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