1.1, 1.2 Home work Statistics

1-1 How is a sample related to a   population? A sample is a subset of a population. What is the difference between a parameter and a statistic? A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic. What are the two main branches of   statistics? The two main branches of statistics are descriptive statistics and inferential statistics. Determine whether the statement is true or false. A statistic is a measure that describes a population characteristic. False. A statistic is a measure that describes a sample characteristic. Determine whether the statement is true or false: A sample is a subset of a population. The statement is true. Determine whether the statement is true or false: Inferential statistics involves using a population to draw a conclusion about a corresponding sample. The statement is false. Inferential statistics involves using a sample to draw a conclusion about a corresponding population. 7- Determine whether the statement is true or false: False. A population is the collection of some   outcomes, responses,   measurements, or counts that are of interest. A population is the collection of all   outcomes, responses,   measurements, or counts that are of interest. 8- Determine whether the following statement is true or false. A sample statistic will not change from sample to sample . The statement is false. A sample statistic can change from sample to sample. 9- Determine whether the data set is a population or a sample. Explain your reasoning. The age of each member of the senate . Population, because it is a collection of ages for all members of the Senate. 10- Determine whether the data set is a population or a sample. Explain your reasoning. The amount of energy collected from every solar panel on a photovoltaic power plant. The data set is a population because it is a collection of the energy collected from all of the solar panels on a photovoltaic power plant. 11- Determine whether the data set is a population or a sample. Explain your reasoning. The heights of half of the students in a class. Sample, because the collection of heights of half of the students is a subset of all students in the class. 12- Determine whether the data set is a population or a sample. Explain your reasoning. The carbon monoxide levels of 23 of 49 people who escaped a burning building . The data set is a sample because the collection of 23 people is a subset of the 49 people who escaped a burning building. 13- Determine whether the data set is a population or a sample. Explain your reasoning. The number of guests in each room of the hotel. The data set is a population because it is a collection of guests for all rooms in a hotel. 14- A survey of 352 automobile owners who purchased extended warranties found that 41% never used the warranty. Identify the population and the sample. Describe the sample data set.

a- Identify the sample for the given problem. Choose the correct answer below. The 352 automobile owners who purchased extended warranties. b- Describe the sample data set. Choose the correct answer below. 41% of the 352 automobile owners who purchased extended warranties but who never used theextended warranty and 59% of the 352 automobile owners who purchased extended warranties and who used the extended warranty. 15- To gather information about starting salaries at companies listed in a stock index, a researcher contacts 78 of the 500 companies. Identify the population and the sample. Describe the sample data set. a- What is the population in the given   problem? The 500 companies in the index. b- Identify the sample for the given problem. Choose the correct answer below. The 78 companies contacted. c- Describe the sample data set. Choose the correct answer below. The starting salaries for 78 companies. 16- Determine whether the underlined value is a parameter or a statistic. In a national survey on substance abuse, 66.4% of respondents who were full-time college students aged 18 to 22 reported using alcohol within the past month. Is the value a parameter or a statistic? Statistic. 17- Suppose a survey of 526 women in the United States found that 60% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey. a- Choose the best statement of the descriptive statistic in the problem. 60% of women in the sample are the primary investor in their household. b- Choose the best inference from the given information. There is an association between U.S. women and being the primary investor in their household. 18- Suppose a survey of 958 car buyers found that 27% bought leather seats. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey. a- Choose the best statement of the descriptive statistic in the problem. 27% of car buyers in the sample bought leather seats. b- Choose the best inference from the given information. Most car buyers do not buy leather seats. 19- A study of 819 senior citizens shows that participants who exercise regularly exhibit less of a decline in the cognitive ability than those who barely exercise at all. From this study, a researcher infers that your cognitive ability increases the more you exercise. What is wrong with this type of reasoning? The inference may incorrectly imply that exercise increases a   person's cognitive ability. The study shows a slower decline in cognitive ability. 20- In a recent study on the effects of sleep and test   results, volunteers took a math test. The volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were   sleep-deprived volunteers. Complete parts a through d. a- Identify the sample used in the study. The sample is the test results of the volunteers in the study .

b- Identify the level of measurement of the data listed on the vertical axis in the figure. Choose the correct answer below . Ratio 10- What is an inherent   zero? Describe three examples of data sets that have inherent zeros and three that do not. a- Select three examples of data sets that have inherent zeros below Maximum wind speed during a hurricane. Average age of college students in years Average monthly precipitation in inches b- Select three examples of data sets that do not have inherent zeros below. Average IQ score of a high school class A student's level of happiness measured from 0 to 10. Temperature in degrees Fahrenheit 1-3 1- What is the difference between an observational study and an   experiment? In an   experiment, a treatment is applied to part of a population and responses are observed. In an observational   study, a researcher measures the characteristics of interest of a part of a population but does not change existing conditions. 2- What is the difference between a census and a sampling? A census includes the entire population. A sampling includes only part of the population. 3- What is the difference between a random sample and a simple random sample? With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected. 4- Determine whether the following statement is true or false. If it is false, rewrite it as a true statement: A placebo is an actual treatment. The statement is false. A placebo is a fake treatment. 5- Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Using a systematic sample guarantees that members of each group within a population will be sampled. False. Using a stratified sample guarantees that members of each group within a population will be sampled . 6- 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. The study is an experiment because it applies treatment to the subjects. 7- Identify the sampling techniques used and discuss potential sources of bias (if any). Explain. Chosen at random, 580 customers at a restaurant were contacted and asked their opinions of the service they received. a- What type of sampling is   used? Simple random sampling is   used, since the business is selecting from its customers at   random, and samples of 580 customers have an equal chance of being selected . b- What potential sources of bias are present, if any? Select all that apply. The wording of the question asked to the customers may influence them towards a particular response. The results would not be usable in this case. 8- Determine whether you would take a census or use a sampling to collect data for the study described below. If you would use a   sampling, determine which sampling technique you would use. Explain. the average height of average height of 120 comma 000120,000 online movie rental subscribers. The study would use a sampling. The study would use simple random sampling because it would be easy for the company to randomly select a portion of its subscribers.

9- Determine if the survey question is biased. If the question is   biased, suggest a better wording. How often do you eat carrots during an average week? No, because it does not lead the respondent to any particular answer . 10- Two types of survey questions are open questions and closed questions. An open question allows for any kind of response; a closed question allows for only a fixed response. An open question and a closed question with its possible choices are given below. List the advantages and disadvantages of each question. Open question: What can be done to get students to eat healthier foods? Closed question: How would you get students to eat healthier foods? 1 . Mandatory nutrition course 2. Offer only healthy foods in the cafeteria and remove unhealthy foods 3. Offer more healthy foods in the cafeteria and raise the prices of unhealthy foods a- What are the disadvantages of an open question? Select all that apply. A. It is difficult to compare the results of surveys with open questions. B. It is difficult to quantify the responses of open questions. C. The form of the question may influence the opinion of the respondent. b- What are the advantages of a closed question? A- It is easy to quantify and compare the results of surveys with closed questions. B. It is possible to automate the collection of results for closed questions. c- What are the disadvantages of a closed question? Select all that apply. A- Closed questions may not provide appropriate alternative responses. B- The form of the question may influence the opinion of the respondent. 2-1: 1- What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions? What are some benefits of representing data sets using frequency distributions ? Organizing the data into a frequency distribution can make patterns within the data more evident. What are some benefits of using graphs of frequency distributions? It can be easier to identify patterns in a data set by looking at a graph of the frequency distribution. 2- Why should the number of classes in a frequency distribution be between 5 and 20? If the number of classes in a frequency distribution is not between 5 and 20, it may be difficult to detect any patterns. 3- What is the difference between class limits and class boundaries? Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer   data, the corresponding class limits and class boundaries differ by 0.5. 4- Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In a frequency distribution, the class width is the distance between the lower and upper limits of a class. False. In a frequency   distribution, the class width is the distance between the lower or upper limits of consecutive classes. 5- Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Class boundaries ensure that consecutive bars of a histogram touch. True a- he approximates number in the sample is 50. b- Choose the correct location of the greatest increase in frequency below. 23.5-24.5 The accompanying data set lists the numbers of children

Choose the correct relative frequency histogram below. Class 62-66 has the greatest relative frequency and class 72- 76 has the least relative frequency. 9- Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative   frequency? Complete the table below. Use the minimum data entry as the lower limit of the first class.

Choose the correct relative frequency histogram below. Class 138 - 202 has the greatest relative frequency and class 3 33- 397 has the least relative frequency. 11- After constructing an expanded frequency distribution, what should the sum of the relative frequencies be? The sum should be   1, since in the sum of the relative frequencies Summation from nothing to nothing Start Fraction f Over n End Fraction ∑ f/n, the numerator will be n= ∑ f.