Exam 1 Study Guide with Practice Problems
Exam 1 Study Guide with Practice Problems STATS 154
Minnesota State University, Mankato
Popular in Elementary Statistics
Popular in Statistics
This 6 page Study Guide was uploaded by Madison Gottschalk on Friday January 22, 2016. The Study Guide belongs to STATS 154 at Minnesota State University - Mankato taught by Mezbahur Rahman in Fall 2016. Since its upload, it has received 90 views. For similar materials see Elementary Statistics in Statistics at Minnesota State University - Mankato.
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Date Created: 01/22/16
Statistics 154 Study Guide: Chapters 1-2 Chapter 1: Sample: a sub-collection of members selected from a population Parameter: a numerical measurement describing some characteristic of a population 1. Determine whether the following statements indicate a parameter or statistic: a. A sample of 90 employees of a company is selected, and the average age is found to be 32 years. b. A researcher determines that 35.2% of all downtown buildings have ventilation problems. c. Based on a sample of 400 patients with high cholesterol, it was found that 69% have heart disease. 2. Determine whether the following statements indicate a parameter or a statistic: a. A researcher determines that all 20 year-olds in her city, 19% are married. b. A researcher examines the records of all the registered voters in one city and finds that 45% are registered Democrats. c. A sample of 40 patients admitted to the emergency room at a hospital, and it is found that 32% have no health insurance. Continuous: Result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps Discrete: Result when the number of possible values is either a finite number or a “countable” number 3. Identify whether the measurement scale in the following statements are continuous or discrete: a. The height of a 3 year-old maple tree b. The total number of phone calls a sales representative makes in a month c. The number of cars passing a busy intersection between 4:30pm and 6:30pm on a Monday d. The temperature in Manhattan at 1:00pm on New Year’s Day e. The average height of all freshmen entering college in a certain year f. The number of stories in a Manhattan building 4. Identify whether the measurement scale in the following statements are continuous or discrete: a. The number of automobile accidents per year in Montana, a state in the USA b. The length of time to complete a phone call c. The quantity of milk produced in a year by a heard of cows d. The number of telephone calls made from a telephone booth e. The weights of truckloads of factory products f. The quantity of soybeans produced per acre Nominal: characterized by data that consists of names, labels, or categorized only, and the data cannot be arranged in an ordering scheme Ordinal: involves data that can be arranged in an order, but differences between data values either cannot be determined or are meaningless. Statistics 154 Study Guide: Chapters 1-2 Interval: involves data that can be arranged in order and the difference between any two data values is meaningful. However, there is no natural zero starting point (none is the quantity present). Ratio: the interval with the additional property that there is also a natural zero starting point (zero indicates that none of the quantity is present); for values at this level, difference and rations are meaningful 5. Identify whether the measurement scale indicated in the following statements is Nominal, Ordinal, Interval or Ratio: a. Survey responses as “good, better, best” b. The temperatures of eight different plastic spheres c. The sample of spheres categorized from softest to hardest d. The colors of cars driven by college students e. Course grades as A, B, C, D or F 6. Identify whether the measurement scales in the following statements are Nominal, Ordinal, Interval or Ratio: a. Nationalities of survey respondents b. Test grades as A, B, C, D of F c. Temperatures of the ocean at various depths d. Survey responses as YES or NO e. Ranking of a tennis player based on total earnings f. Year of a historical event Experimental: apply some treatment and then observe its effects on the subjects Observational: observing and measuring specific characteristics without attempting to modify the subjects being studied 7. Identify whether the following statements indicate the data are experimental or observational: a. A marketing firm does a survey to find out how many people use a product. Of the 100 people contacted, 15 say they use the product. b. A quality control specialist compares the output from a machine with a new lubricant to the output of machines with the old lubricant. c. A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided. d. A stock analyst selects a stock from a group of 20 for investment by choosing the stock with the greatest earning per share reported for the last quarter. e. A clinic gives a drug to a group of 10 patients and a placebo to another group of 10 patients to find out if the drug has an effect on the patient’s illness f. A sample of fish is taken from a lake to measure the effect of pollution from a nearby factory on the fish 8. Identify whether the following statements indicate the data are experimental or observational: a. Investigation of the relationships between the occurrence of sickle-cell anemia and ethnic background b. Evaluation of a new technique of teaching first graders to read Statistics 154 Study Guide: Chapters 1-2 c. A study of female college graduates who go to graduate school d. A study of accident rates in urban areas e. Determination of the effectiveness of an advertising program f. Evaluation of the new lighting system in a factory work area Random: a sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen Stratified: subdivide the population into at least 2 different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum) Systematic: select some starting point and then select every kth element in the population Cluster: divide the population area into sections (or clusters). Then randomly select some of those clusters and choose all members from selected clusters. Convenience: use results that are easy to get 9. Classify the following sampling methods indicated by the respective statements as either random, stratified, systematic, cluster or convenience: a. To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day b. An education researcher randomly selects 48 middle schools and interviews all the teachers at each school. th c. A tax auditor selects every 100 income tax return that is received. d. A researcher randomly selects 300 drivers less than 25 years of age and 400 drivers over 25 years of age e. A researcher interviews 19 work colleagues who work in his building f. A pollster uses a computer to generate 420 random numbers and interviews the voters corresponding to those numbers 10. Classify the following sampling methods indicated by the respective statements as either random, stratified, systematic, cluster or convenience: th a. A complete list of all stockholders is compiled, and every 500 name is selected from each brokerage house. b. At the annual stockholders’ meeting, a survey is conducted of all who attended c. Five different brokerage houses are randomly selected, and a survey is made of all their clients who won shares of Coca Cola. d. A computer file of all stockholders is compiled so that they are all numbered consecutively, then random numbers generated by computer are used to select the sample of stockholders e. All of the stockholders’ zip codes are collected, and five stockholders are randomly selected from each zip code 11. Select a random sample of 12 households from 150 neighborhood households using the random number table, Table 1 in Appendix 2. Start with a random starting point and do not forget to mention the starting point. Statistics 154 Study Guide: Chapters 1-2 12. Select a stratified random sample of 30 students consisting of 12 males and 18 females from your school. There is a total of 2,000 students consisting of 800 males and 1,200 females. Use Table 1 in Appendix 2. Describe the method. 13. In a modern township, there are 200 high rise apartment buildings. Explain the complete survey procedure. Chapter 2: 1. The following are hypothetical data from small four-year college: Male Female Total Freshmen 329 400 729 Sophomores 177 171 348 Juniors 150 111 261 Seniors 142 83 225 Total 798 765 1563 a. Present these data by gender in a bar chart. b. Present these data by gender in two pie charts for the two genders. 2. A small toy company recorded the following information concerning last year’s operating expenses: Item Expenditures Cost of products sold $150,000 Administrative expenses 25,000 Commissions 75,000 Interest 10,000 Depreciation 60,000 Income taxes 40,000 a. Present these data ion a bar chart b. Present these data in a pie chart 3. At the end of its first year of operations, a new credit union has 60 accounts in US dollars as shown below: Statistics 154 Study Guide: Chapters 1-2 50 300 510 720 950 1250 50 350 550 750 1000 1250 70 370 560 750 1000 1250 120 380 560 800 1000 1270 150 390 570 800 1000 1280 150 400 580 800 1010 1290 200 500 580 810 1050 1300 250 500 600 820 1080 1350 260 500 600 820 1090 1380 280 500 630 830 1090 1400 a. Construct a stem-lead display b. Construct a frequency table and a histogram c. Construct a box-plot and comment on whether there is any outlier(s). 4. The following data are on ages of women working at a garment factory: 43 58 21 24 31 49 40 51 55 28 50 33 62 30 25 39 59 29 36 42 38 46 42 18 50 41 37 35 40 52 47 35 57 55 50 36 45 32 45 42 36 52 64 34 32 47 41 44 39 38 a. Construct a stem-leaf display b. Construct a frequency table c. Construct a box-plot and comment on whether there is any outlier(s) 5. An electrical company has developed and is about to market a new “long-life” light bulb. They would like to make a statement about the “average life” of their bulbs. Since the company is mostly short on everything, including money, they have decided to base any statement they make on a sample of 10 bulbs. As the company’s statistician, you are given the following data on the “life” of the 10 bulbs. 106 99 78 110 97 82 15 86 108 97 a. Compute the arithmetic mean b. Compute the median c. Compute the mode d. Compute the standard deviation e. Compute the mean absolute deviation f. Compute the z-score for the minimum value of the data and comment on whether it is unusual or not Statistics 154 Study Guide: Chapters 1-2 6. A consumers’ interest magazine reports the following observed values of octane ratings for low- lead gasoline: 90.3 90.9 91.9 87.9 89.1 87.1 87.7 90.7 88.3 87.8 90.6 91.6 87.6 90.5 88.1 90.4 90.1 89.8 87.4 90.8 89.3 89.9 88.2 88.4 87.5 a. Compute the arithmetic mean b. Compute the median c. Compute the mode d. Compute the standard deviation e. Compute the mean absolute deviation f. Compute the z-score for the maximum value of the data and comment on whether it is unusual or not 7. Mr. Peters, the owner-manager of Peters Fish & Chips, had recently received complaints from some of his customers regarding how long they had to wait for service at the drive-in window. Picking the busiest time of day, Mr. Peters recorded the following times in minute, from arrival to service completion, for 10 customers. 3.2 15.1 10.9 8.3 8.8 2.5 9.4 12.7 18.4 6.6 Calculate the mean waiting time and the standard deviation of the waiting time. 8. In the small community of Robersonville there are 11 families—Mr. Robinson and his 10 employees. The following is a list of the family incomes in the community for the last year: $50,000 $70,500 $50,500 $90,000 $70,000 $1,000,000 $78,000 $62,500 $100,000 $150,000 $85,000 Calculate the mean income and the standard deviation of the income.
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