STA 13 Fall 2023 - Homework Week 1

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University of California, Davis *

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013

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Statistics

Date

Feb 20, 2024

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pdf

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STA 13 Fall 2023 - Homework Week 1 Name: Qiyuan Mao Student ID: 922015416 a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate. 42. A fitness center is interested in the mean amount of time a client exercises in the center each week. a. The population: all clients of the fitness center. b. The sample: a random selection of 100 clients. c. The parameter: the mean amount of time all clients exercise in the center each week. d. The statistic: the mean amount of time the selected clients exercise in the center each week. e. The variable: the amount of time the client exercises per week. f. The data: the actual exercise time of the sampled clients, such as one hour, two hours, etc. 44. A cardiologist is interested in the mean recovery period of her patients who have had heart attacks. a. The population: all the patients who have had heart attacks and are treated by the cardiologist. b. The sample: a random selection of 50 patients who have had heart attacks and are treated by the cardiologist. c. The parameter: the mean recovery period of all the patients who have had heart attacks and are treated by the cardiologist. d. The statistics: the mean recovery period of the selected patients who have had heart attacks and are treated by the cardiologist. e. The variable: the recovery period of the patient after having heart attacks. f. The data: the actual recovery periods of selected patients after having heart attacks, such as one week, two weeks, etc. 46. A politician is interested in the proportion of voters in his district who think he is doing a good job. a. The population: all voters in the politician's district. b. The sample: a random selection of 1000 voters in the politician’s district. c. The parameter: the proportion of all voters in the politician’s district who think he is doing a good job. d. The statistics: the proportion of the selected voters in the politician’s district who think he is doing a good job. e. The variable: the voters’s opinion about the politician’s performance. f. The data: the actual responses from the selected voters, such as good job or not good job. For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

54. percent of body fat : Quantitative continuous data, for example, 18.876% of fat. 56. time in line to buy groceries : Quantitative continuous data, for example, 3.7653 minutes. 58. most-watched television show : Qualitative data, for example, Apollo 11 Moon landing. 66. Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed. By employing the systematic random sampling method, the mean number of students can be determined. First, make a list of all the statistics classes in the state, noting how many students are in each class. Then, start by picking a random class from the list. After that, choose every nth class to include in your sample. You figure out n by dividing the total number of classes by the size of the sample you want. This systematic approach ensures that you obtain a representative sample from across the state. a. Fix the errors in Table 1.35. Also, explain how someone might have arrived at the incorrect number(s). Data Frequency Relative Frequency Cumulative Relative frequency 0 2 2/19 0.1053

2 3 3/19 0.2632 4 1 1/19 0.3158 5 3 3/19 0.4737 7 2 2/19 0.5789 10 2 2/19 0.6842 12 2 2/19 0.7895 15 2 2/19 0.8948 20 2 2/19 1 The incorrect numbers might have resulted from a simple calculation error or a typo when entering the data into the table. b. Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.” 47% refers to the cumulative relative frequency of immigrants who have been in the United States for zero years, two years, four years, and five years combined, not just 47% of the 19 who have been in the United States for five years. c. Fix the statement in b to make it correct. The corrected statement should be: "47 percent of the people surveyed have lived in the U.S. for either zero years, two years, four years, or five years." Or 15.79 percent of the people surveyed have lived in the U.S for five years. Or 53 percent of the people surveyed have lived in the U.S for five years or more. d. What fraction of the people surveyed have lived in the U.S. five or seven years? 3 (5 year) + 2 (7 year) = 5 people So, 5 out of the 19 people surveyed have lived in the U.S. for either five or seven years. e. What fraction of the people surveyed have lived in the U.S. at most 12 years? 2+3+1+3+2+2+2 = 15 people So, 15 out of the 19 people surveyed have lived in the U.S. for at most 12 years f. What fraction of the people surveyed have lived in the U.S. fewer than 12 years? 2+3+1+3+2+2=13 people So, 13 out of the 19 people surveyed have lived in the U.S. for at most 12 years g. What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive? 3+2+2+2+2+2=13 people

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