MT – 221 MATH
MT221. with the drug. Assuming that the 5000 individuals are representative of the group that has hypertension, answer the following questions: 1) International Communications Research (IRC) conducted the 2008 Spring Cleaning Survey for the Soap and Detergent Association. IRC QUESTIONED 777 American adults who springclean about which spring- cleaning chore they would like to hire someone to do for them. The “chore” results were: 47% washing windows, 23% cleaning the bathroom, 12% cleaning the kitchen, 8% dusting, 7% mopping, 3% other. The survey has a margin of error of plus or minus 3.52%. a. What is the population? b. What is the sample? c. Identify the parameter of interest. d. Identity the statistic and give its value. e. Do we know the value of the parameter? a. What is the population? b. How many people were polled? c. What information was obtained from each person? d. Using the information given, estimate the number of surveyed adults who would gladly hire someone to wash the windows, if they could. e. What do you think the “margin of error of plus or minus 3.52%” means? f. How would you use the “margin of error” in estimating the percentage of all adults who would like to hire out the spring- cleaning chore of “Cleaning the kitchen”? 2) During a radio broadcast a few years ago, David Essel reported the following three statistics: (1) the U.S divorce rate is 55%, and when married adults were asked if they would remarry their spouse, (2) 75% of the women said yes, and (3) 65% of the men said yes. a. What is the “stay married” rate? b. There seems to be a contradiction in this information. How is it possible for all three of these statements to be correct? Explain. 3) A drug manufacturer is interested in the proportion of persons with hypertension (elevated blood pressure) whose condition can be controlled by a new drug the company has developed. A study involving 500 individuals with hypertension is conducted, and it is found that 80% of the individuals are able to control their hypertension 4) In July 8, 2019, USA Today article titled “Couples saying’ I don’t to expensive weddings,” the cutbacks may not be extending to the number of bridesmaids was as follows: 7 6 5 2 3 7 6 13 6 3 2 7 8 9 a. Construct a dotplot of these data. b. What are the most common numbers of bridesmaids? How does the dotplot show this? 4) Some cleaning jobs are disliked more than others. According to the July 17,2009, USA Today Snapshot on a survey of women by Consumer Reports National Research Center, the cleaning tasks women dislike the most are presented in the following Pareto diagram. a. How many total women were surveyed? b. Verify the 15% listed for “Cleaning refrigerator.” c. Explain how the “cu, % for dusting” value of 80% was obtained and what it means. d. What three tasks would make no more than 75% of the women surveyed happy if those tasks were eliminated? 5) Fill in the Blank: (Statistics, Data, Descriptive Statistics, Inferential Statistics, Probability, Population, Samples, Parameter) a) ( )-the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data. b) ( ) – collections of observations. c) ( ) – organizing and summarizing data; by graphing and by numerical values (such as an average). d) ( )- uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result. e) ( )- the chance of an event occurring. f) ( )- the complete collection of all individuals to be studied. g) ( ) – a subcollection of members selected from a population. Example: h) ( ) – a numerical measurement describing some characteristic of a population. Ex: The average age of students enrolled as an undergraduate at Baylor University is 21.1 years. 6) Identify each of the following as examples of (1) attribute (qualitative) or (2) numerical (quantitative) variables: a) Th breaking strength of a given type of string b) The hair color of children auditioning for the musical Annie c) The number of stop signs in towns of fewer than 500 people d) Whether or not a faucet is defective e) The number of questions answered correctly on a standardized test f) The length of time required to answer a telephone call at a certain real estate office. 7) What is the mean weekly pay if 5 employees earn $425 per week, 3 earn $750 per week, and 1 earns $1340? 8) A city police officer, using radar, checked the speed of cars as they were traveling down the main street in town. Construct a stem-and-leaf plot for this data: 41 31 33 35 36 37 39 49 33 19 26 27 24 32 40 39 16 55 38 36 9) A survey of 100 resort club managers on their annual salaries resulted in the following frequency distribution. Ann. 15Sal.($1000) 25 No. Mgrs 12 2535 37 3545 26 4555 19 5565 6 a. Prepare a cumulative frequency distribution for the annual salaries. b. Prepare a cumulative relative frequency distribution for the annual salaries. c. Construct an ogive for the cumulative relative frequency distribution found above. d. What value bonds the cumulative relative frequency of 0.75? e. 75% of the annual salaries are below what value? Explain the relationship between parts d and e. 10) For those seventh graders with cell phones, the number of programmed numbers in their phones are: 100 37 12 20 53 10 20 50 35 30 a) Find the mean number of programmed numbers on a seventh grader’s cell phone. represents the value of the standard deviation f) Describe how the distribution of data, the range, and the standard deviation are related. b) Find the median number of programmed numbers on a seventh grader’s cell phone c) Explain the difference in values of the mean and median. d) Remove the most extreme value and answer parts a through c again. e) Did removing the extreme value have more effect on the mean or the median? Explain why. 13) Following are the American College Test (ACT) scores attained by the 25 members of a local high school graduating class: 21 24 23 17 31 19 19 20 19 25 17 23 16 21 28 25 25 21 14 19 17 18 28 20 20 a) Using the concept of depth, describe the position of 24 in the set of 25 ACT scores in two different ways. b) Find 𝑃” ,𝑃#$, and 𝑃!$ for the ACT scores. 11) Consider the sample 2,4,7,8,9. Find the following c) Find 𝑃&& , 𝑃&$ and 𝑃’$ for the ACT scores. A research study of manual dexterity involved determining the time requires to complete a task. The time required for each of 49 individuals with disabilities is shown here (data are ranked): A. mean, 𝑥̅ B. median, 𝑥# C. mode D. midrange 11) Consider the sample 6,8,7,5,3,7. Find the following 13) A. Range B. Variance𝑠 ! , using formula (2.5) C. Standard deviation, s 12) Recruits for a police academy were required to undergo a test that measures their exercise capacity. The exercise capacity (in minutes) was obtained for each 20 recruits: 25 26 27 30 33 30 32 30 34 30 27 25 29 31 31 32 34 32 33 30 a) Find the mean. b) Find the range. c) Find the variance. d) Find the standard deviation e) Using the dot-plot from part a, draw a line representing the range. Then draw a line starting at the mean with the length that 7.1 7.2 7.2 7.6 7.6 7.9 8.1 8.1 8.1 8.3 8.3 8.4 8.4 8.9 9.0 9.0 9.1 9.1 9.1 9.1 9.4 9.6 9.9 10.1 10.1 10.1 10.2 10.3 10.5 10.7 11.0 11.1 11.2 11.2 11.2 12.0 13.6 14.7 14.9 15.5 a) Find 𝑄# . b) Find 𝑄! c) Find 𝑄( d) Find 𝑃&” e) Find the 5- number summary. f) Draw the box-and-whisker display. 14) A sample has a mean of 50 and a standard deviation of 4.0. Find the z-score for each value of x: A. x = 54 B. x=50 C. x =59 D. x = 45 15) An exam produced grades with a mean score of 74.2 and a standard deviation of 11.5. Find the z-score for each test score x: A. x=54 B. x=68 C. x=79 D. x=93 16) A sample has a mean of 120 and a standard deviation of 20.0. Find the value of x that corresponds to each of these standard scores: A. Z =0.0 B. Z=1.2 C. Z= -1.4 D. Z=2.05 17) The empirical rule indicates that we can expect to find what proportion of the sample included between the following : A. 𝑥̅ – s and 𝑥$ + s B. 𝑥$ -2s and 𝑥̅ + 2s C. 𝑥̅ – 3s and 𝑥$+ 3s 18) The final daily inspection defect report for a cabinet manufacturer is given in the table below: a) Construct a Pareto diagram for this defect report. Defect Number Dent 5 Stain 12 Blemish 43 Chip 25 Scratch 40 Others 10
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