# Statistics Topics

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Statistics

StatisticsIn your new role as a data analyst for a larg hospital patient outcomes at a newly built hospital Mountain View versus an existing hospital Greenside She is specifically interested in seeing whether patients who are seen for heart attacks are being readmitted to the hospital more often in the new facility You looked at data from a random sample of visits to the two hospitals during the last year Hospital Site Visited Was Patient Readmitted to the Hospital within 30 days following treatment for heart attack Yes No Total 7 40 O 29 63 54 00 Mountain View Greenside Total 07118 54 705 759 16 171 187 70 If you choose a person from the sample at random what is the probability that the person was readmitted to the hospital within 30 days following treatment for heart attack 876 946

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StatisticsHospital administrators want to determine the average satisfaction for patients receiving care in the ER over the last month The list of all ER patients over the last month is entered into a computer program which uses an algorithm to randomly select 100 patients Surveys are then sent to those patients What type of sampling method is this O Systematic Random O Multistage cluster Simple Random

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ProbabilityA group of 262 students was polled to determine whether they exercise regularly engaging in moderate activity for 30 60 min 3 or more times per week Exercises Regularly No Yes Total 50 38 49 62 Female O 54 31 O 61 70 72 58 130 Gender Male 96 36 132 Total 168 If you choose a person from the survey at random what is the probability that the person is male 94 262

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ProbabilityWhich of the following is concerned with monitoring estimates of present performance and predictions of future performance O Construct validity Criterion validity O Content validity O Internal validity

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StatisticsResearchers want to determine the percentage of students who own iPhones and Android cell phones They go to a popular spot on campus and ask first 100 students who pass what type of cell phone they own What type of sampling method is this Convenience O Stratified O Random O Cluster

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ProbabilityIn a box there are 8 red 7 blue and 6 green balls One ball is picked up randomly What is the probability that it is neither red nor green O 14 21 O 3 4 O 1 3 O 7 19

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StatisticsTrue or False reliability refers to whether we are truly measuring what we are trying to measu True False

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Probabilityeducational backgrounds of the channel s viewers are different from the educational backgrounds of American adults ages 25 and over as a whole The executives have the following information on the American adult population as a whole obtained from a recent U S Current Population Survey Highest degree earned Less than high school High school College Higher than college Percent of population 8 The executives also obtained data from telephone surveys on highest degrees earned for a random sample of 150 American adults who are Thinking Channel viewers These data are summarized by the first row of numbers in the table below These numbers are the frequencies for the degree categories that were observed in the sample of 150 The second row of numbers gives the expected frequencies under the assumption that the distribution of highest degrees earned by Thinking Channel viewers is the same as the distribution of highest degrees earned by American adults as a whole The bottom row of numbers gives the following value for each of the degree categories fo SE Observed frequency Expected frequency Expected frequency fe Send data to Excel Observed frequency fo Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your fo B responses to three or more decimal places Expected frequency JE 12 fo fe JE Less than high school 13 0 High school 25 27 0 10 College 101 82 50 55 4 148 a Determine the type of test statistic to use Higher than college 9 12 00 0 750 Total 150 Part 2 Answer the following to summarize the test of the hypothesis that the distribution of highest degrees earned by Thinking Channel viewers is the same as the distribution of highest degrees earned by American adults as a whole Use the 0 10 level of significance for the test X Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places 0 d Can we conclude that the distribution of highest degrees earned by Thinking Channel viewers is different from the distribution of highest degrees earned by American adults as a whole As

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StatisticsWhich of the following are TRUE about the sampling frame choose one or more Osampling frame enumerated list of population It is the group from which the sample is drawn sampling frame a summary of the sample that is drawn from the population The registrar at ASU could provide a sampling frame of the population of current ASU students

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StatisticsTrue or False the probability of an outcome can be a negative number O True False

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Statisticscommon during some parts of the year than others Owners of a children s toy store chain asked this question Some data collected by the chain are summarized in the table below The data were obtained from a random sample of 190 people The birthdate of each person was recorded and each of these dates was placed into one of four categories winter December 21 March 20 spring March 21 June 20 summer June 21 September 20 and fall September 21 December 20 The numbers in the first row of the table are the frequencies observed in the sample for these season categories The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year The bottom row of numbers gives the following value for each of the season categories So Se JE Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo JE responses to three or more decimal places fe Send data to Excel Observed frequency lo Expected frequency JE Observed frequency Expected frequency Expected frequency So Se fe Winter Spring Summer 35 0 0 45 0 0 44 47 50 0 258 Fall Total 66 47 50 7 205 a Determine the type of test statistic to use 190 X Part 2 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year Use the 0 05 level of significance the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the p value Round your answer to three or more decimal places 0 d Can we reject the hypothesis that birthdays are equally likely during each season of the year 6 E

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StatisticsThe Ellington Dukes team AS WIL other minor league teams the Dukes rely heavily on promotions to bring fans to the ballpark These promotions are typically aimed at fans of specific ages The management for the Dukes has planned its current promotional schedule according to the following estimates 15 of fans attending Dukes games are ages o to 12 10 are ages 13 to 18 30 are ages 19 to 35 25 are ages 36 to 5s and 20 are over 55 A statistical consulting firm for the Dukes surveyed a random sample of 200 fans attending Dukes games in order to see if these estimates are accurate For the sample of 200 the observed frequency of each age category is given in the top row of numbers in the table below The second row of numbers contains the frequencies expected for a random sample of 200 fans if the Dukes management s estimates are accurate The bottom row of numbers contains the following value for each of the age categories fo E Observed frequency Expected frequency Expected frequency Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo 18 2 responses to three or more decimal places Send data to Excel Observed frequency fo Expected frequency JE SE o to 12 34 13 to 18 28 0 19 to 35 61 60 00 0 017 36 to 55 30 50 00 8 000 Over 55 a Determine the type of test statistic to use 47 40 00 1 225 Total 200 X Part 2 Answer the following to summarize the test of the hypothesis that the management s estimates are accurate Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places 0 S d Can we conclude that the management s original estimates for the age distribution of fans attending Dukes games are inaccurate OYes No X

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StatisticsA somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44 We have good reason to suspect that the mean number of hours worked per week by software developers is now greater than 44 and wish to do a statistical test We select a random sample of software developers and find that the mean of the sample is 47 hours and that the standard deviation is 3 hours Based on this information complete the parts below a What are the null hypothesis Ho and the alternative hypothesis H that should be used for the test H 0 H 0 b Suppose that we decide not to reject the null hypothesis What sort of error might we be making Choose one c Suppose the true mean number of hours worked by software engineers is 44 hours Fill in the blanks to describe a Type I error A Type I error would be Choose one the hypothesis that u is Choose one Choose one when in fact is Choose one equal to 3 equal to 44 less than 3 less than 44 greater than 44 H X 0 0 OSO X O O 020 0 0 0 0 G

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StatisticsThe weight of an organ in adult males has a bell shaped distribution with a mean of 310 grams and a standard deviation of 45 grams Use the empirical rule to determine the following a About 95 of organs will be between what weights b What percentage of organs weighs between 175 grams and 445 grams c What percentage of organs weighs less than 175 grams or more than 445 grams d What percentage of organs weighs between 175 grams and 400 grams

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Statisticsmean hourly wage of foodservice workers in the U S this year The mean hourly wage last year was 8 25 and there is good reason to believe that this year s value is different from last year s The union decides to do a statistical test to see if the value has indeed changed The union chooses a random sample of this year s wages computes the mean of the sample to be 7 85 and computes the standard deviation of the sample to be 1 25 Based on this information complete the parts below a What are the null hypothesis H and the alternative hypothesis H that should be used for the test Ho D H 0 b Suppose that the union decides not to reject the null hypothesis What sort of error might it be making Choose one c Suppose the true mean hourly wage for foodservice workers in the U S this year is 8 25 Fill in the blanks to describe a Type I error A Type I error would be Choose one Choose one Choose one equal to 1 25 equal to 7 85 equal to 8 25 not equal to 8 25 less than 1 25 the hypothesis that u is Choose one when in fact is H 0 0 ORO X X OSO 0 0 O 0

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Statistics150 135 170 175 135 140 134 130 175 160 120 125 103 170 110 140 120 150 129 150 The number of calories contained in 20 randomly selected scoops of ice cream is shown above Construct a grouped frequency distribution for the data Construct the frequency distribution with five classes and let the first class begin with 103 Once you have completed your frequency distribution answer the following questions