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# Elemntry Statistical Inference STAT 211

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This 18 page Class Notes was uploaded by Lilly Rutherford on Saturday September 12, 2015. The Class Notes belongs to STAT 211 at West Virginia University taught by Anthony Billings in Fall. Since its upload, it has received 23 views. For similar materials see /class/202822/stat-211-west-virginia-university in Statistics at West Virginia University.

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Date Created: 09/12/15

Stat211 Practice Exam 3 Final Exam n nn 121 2 2 SSy 2y2 2y W n n m quot1 quot m SSxy Exy m my y rel freq ifmq39 n r SSxy X VSSXSSy n 2 my may M 7x r n N 2x2 2201 zyz 32 11 n 2 S mma 2X43 7 7 J n rltwzxx1yyj n 1 SX Sy 20 2 1 1 2 a N r n1 Sy x xy y 2 2x 32MM n ybob1x n 1 n 1 b SSW 2 SSx 02 m u m may n 2x2 202 7n 1 n 7 S skew 30C x b1 r 3 IQRZQ3Q1 b0yblf ZXM residualy 7 7 SSE 2y W 2 SSx 2x2 Q 2x 1 02 n Stat211 Practice Exam 3 Final Exam PA L m 13A 5 n PnotA1 PA PA U B PA PB PAn B PA U B PA PB PAn B PA PB I A PA r B PB PA I B PA r B PA PB pABm PA n B PA PBIA PA PA B and PB PB IA E00 u 2xpx EX M n p of m My pm a Vibe 92 poo n PX PxUpyk x 012n x Mnp 0 vnp p 13 x e 2718281828 7 x PX g 012 X M A a a p501n225np510 np np gt 5 n1 pgt 5 x truevalue bias randomerror EMbias Stat211 Practice Exam 3 Final Exam 76 CritValSE S 7c z 7 4 3 LJ 4 n13gt5n1 f gt5 170 P f7 zSEf7 For 90 CL 221645 For 95 CL 221960 For 99 CL 222578 B U m n iM S 1 2 2 S fyiz 34 n m If wirmw smLi n m dfnm 2 n 1Sx2m 1Sy2 S nm 2 t n131gt5 Ila 131 gt5 m 2gt5 m1 32 gt 5 1311 131 1321 132 n m 131 132iz Stat211 Practice Exam 3 Final Exam A xy 7 17 p nm p1 p n aPTypeI PT I TXM0 B ypeI a dfk 1 Zx Mo 0 2 7 2 O E W X E T E W E rowtotal columntoml id n V E row l column Tx y Mx My 7 n 1 1 Sp 2 dfr 1c 1 0 E 052 ZzTx y MxMy X2E g 2 2 sx i m Z 131 130 171 172 130 be i n m Stat211 Practice Exam 3 Final Exam 1 The average length of workweeks of 15 randomly selected employees in the mining industry and 10 randomly selected employees in the manufacturing industry were obtained The sample mean and sample deviation for each sample are given in the table below Sample Observations Mean Std Dev Miners Sample X 15 475 55 Manufacturers Sample Y 10 425 49 A 95 confidence interval for the difference MX My a goes from 078 hours to 922 hours b goes from 131 hours to 869 hours c goes from 088 hours to 912 hours d goes from 055 hours to 945 hours e goes from 065 hours to 935 hours 2 The average length of workweeks of 15 randomly selected employees in the mining industry and 10 randomly selected employees in the manufacturing industry were obtained The sample mean and sample deviation for each sample are given in the table below Sample Observations Mean Std Dev Miners Sample X 15 475 55 Manufacturers Sample Y 10 425 49 A 95 confidence interval for the difference MX My a requires that the critical value in the error term comes from a t distribution with 23 degrees of freedom b requires that the critical value in the error term comes from a t distribution with 25 degrees of freedom c does not require that the pooled standard deviation be computed d cannot be calculated with the information provided e none of the above 3 The average length of workweeks of 15 randomly selected employees in the mining industry and 10 randomly selected employees in the manufacturing industry were obtained The sample mean and sample deviation for each sample are given in the table below Sample Observations Mean Std Dev Miners Sample X 15 475 55 Manufacturers Sample Y 10 425 49 Suppose that a 95 confidence interval for the difference MX My goes from 054 hours to 946 hours We can say that Stat211 Practice Exam 3 Final Exam a 95 of all miners work between 054 hours and 946 hours longer per week than 95 of all manufacturers on the average b we are 95 confident that the sample of 15 miners works between 054 hours and 946 hours longer per week than the sample of 10 of manufacturers on the average c we are 95 confident that on the average the population of miners works between 054 hours and 946 hours longer per week than the population of manufacturers d there is a 95 probability that miners average workweek is between 054 hours and 946 hours longer than a manufacturer s workweek e none of the above 4 Suppose a researcher performs a test of H0 u 100 vs H A u lt 100 Which of the following statements is correct a An extremely small p value indicates that the actual data differs significantly from that which would be expected if the null hypothesis were true b The p value measures the probability that the hypothesis is true c The larger the p value the stronger the evidence against the null hypothesis d A large p value indicates that the data is consistent with the alternative hypothesis e None of the above 5 A random sample of 10 observations is selected from a normal distribution with population mean equal to 75 and population standard deviation equal to 20 Then the distribution of possible values of the sample mean a cannot be determined from the information provided b will not be normal because the sample size is too small c will be normal d will not be normal because the population size is too small e none of the above 6 A neurologist wants to determine if the use of alcohol increases reaction time The reaction time in seconds of a group of 6 randomly selected adults was measured before and after consuming two alcoholic beverages The observed data is in the following table Adult Reaction Time Before Reaction Time After Difference 39 Alcohol C 39 Alcohol After Before 1 08 13 05 2 05 12 07 3 09 19 10 4 07 16 09 5 06 15 09 6 08 16 08 Stat211 Practice Exam 3 Final Exam The sample mean difference is 08 seconds with a sample standard deviation of 01789 seconds The neurologist will perform a test of hypothesis to determine if the consumption of alcohol increases reaction time The alternate hypothesis would be a HA ux My0 b HA ux Mylt0 c H A Md gt 0 d HA Md 2 08 e HA MX MYgt0 7 A neurologist wants to determine if the use of alcohol increases reaction time The reaction time in seconds of a group of 6 randomly selected adults was measured before and after consuming two alcoholic beverages The observed data is in the following table Adult Reaction Time Before Reaction Time After Difference 39 Alcohol C 39 Alcohol After Before 1 08 13 05 2 05 12 07 3 09 19 10 4 07 16 09 5 06 15 09 6 08 16 08 The sample mean difference is 08 seconds with a sample standard deviation of 01789 seconds The neurologist will perform a test of hypothesis to determine if the consumption of alcohol increases reaction time The value of the test statistic rounded to the nearest hundredth is a 1095 b 1095 c 447 d 447 e cannot be determined with the information provided 8 A neurologist wants to determine if the use of alcohol increases reaction time The reaction time in seconds of a group of 6 randomly selected adults was measured before and after consuming two alcoholic beverages The observed data is in the following table Adult Reaction Time Before Reaction Time After Difference C 39 Alcohol C 39 Alcohol After Before 1 08 13 0 5 2 05 12 0 7 3 09 19 1 0 4 07 16 0 9 5 06 15 0 9 6 08 16 0 8 Stat211 Practice Exam 3 Final Exam The sample mean difference is 08 seconds with a sample standard deviation of 01789 seconds The neurologist will perform a test of hypothesis to determine if the consumption of alcohol increases reaction time using a significance level of OL 005 Suppose that p value of the test statistic is 00143 Then the neurologist would a accept the null hypothesis b reject the null hypothesis 0 fail to reject the null hypothesis d fail to reject the alternate hypothesis e none of the above 9 A random sample of 100 voters in a community produced 59 voters in favor of candidate A The observed value of the test statistic for testing the null hypothesis Ho p 205 versus the alternative hypothesis H A pgt05 is a 180 b 190 c 183 d 128 e 175 10 An automobile dealer believes that certain colors of cars are more popular than other colors He randomly selects 60 sales records from the previous year and records the color of each car sold The data is displayed in the table below Color Observed Freq uech Red Blue 12 White 13 Black 14 A hypothesis test is performed in order to determine if the data supports the claim of the automobile dealer The alternate hypothesis would be a HA The color blue has a lower preference than the other colors b 171A At least one color is preferred differently than the other colors 0 H A The color red has a higher preference than the other colors d HA All colors are equally preferred e none of the above 11 An automobile dealer believes that certain colors of cars are more popular than other colors He randomly selects 60 sales records from the previous year and records the color of each car sold The data is displayed in the table below Color Observed Freq uech Red Blue 12 White 13 Black 14 Stat211 Practice Exam 3 Final Exam A hypothesis test is performed in order to determine if the data supports the claim of the automobile dealer The value of the test statistic rounded to the nearest hundredth is a 240 b cannot be calculated with the information provided c 333 d 333 e none of the above 12 An automobile dealer believes that certain colors of cars are more popular than other colors He randomly selects 60 sales records from the previous year and records the color of each car sold The data is displayed in the table below Color Observed Freq uech Red Blue 12 White 13 Black 14 A hypothesis test is performed in order to determine if the data supports the claim of the automobile dealer using a significance level of 010 Suppose that the researcher fails to reject the null hypothesis Then the researcher would state hisher conclusion as a at the 10 significance level there does not seem to be a significant difference in the preference between car colors b at the 10 significance level there does seem to be a significant difference in the preference between car colors 0 at the 10 significance level the color red seems to have a higher preference than the other car colors d at the 10 significance level the color blue seems to have a lower preference than the other car colors e none of the above 13 The following data were obtained from an experiment designed to estimate the change in cholesterol level as a result of a nutrition education class Before After 295 279 250 235 255 290 310 260 265 266 245 240 230 250 240 250 A 90 confidence interval on the mean difference Before After a goes from 763 points to 3937 points b goes from 370 points to 4330 points 0 goes from 580 points to 5280 points d goes from 709 points to 3991 points e goes from 1165 points to 3535 points Stat211 Practice Exam 3 Final Exam 14 The following data were obtained from an experiment designed to estimate the change in cholesterol level as a result of a nutrition education class Before 295 279 250 235 255 290 310 260 After 265 266 245 240 230 250 240 250 Suppose that a 90 confidence interval on the mean difference Before After goes from 1165 points to 3535 points The appropriate interpretation is that a 90 of all students of this nutrition class exhibit a reduction in cholesterol level between 1165 points and 3535 points b we are 90 confident that the sample of 8 students in the nutrition class exhibit a reduction in cholesterol level between 1165 points and 3535 points on the average c we are 90 confident that the average reduction in cholesterol level as a result of the nutrition class is between 1165 points and 3535 points d there is a 90 probability average reduction in cholesterol level as a result of the nutrition class is between 1165 points and 3535 points e 90 of all students of this nutrition class exhibit an increase in cholesterol level between 1165 points and 3535 points 15 The following are grams of fat found in 5 scoops of each of two brands of ice cream A 57 45 62 63 73 B 63 57 59 64 51 Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream a Paired T test with 5 df b Two sample T test with 8 df c Paired T test with 4 df d Two sample T test with 9 df e none of the above 16 A manufacturer of automobile tires believes that a new rubber compound will increase the safety of the tires A quality assurance specialist must decide between the null hypothesis The new rubber compound has no beneficial effects on tire safety and the alternate hypothesis The new rubber compound increases tire safety A type I error would be a the quality assurance specialist decides that the new rubber compound has no beneficial effects on tire safety when it actually does not have any beneficial effects b the quality assurance specialist decides that the new rubber compound does increase tire safety when it actually does not have any beneficial effects c the quality assurance specialist decides that the new rubber compound has no beneficial effects on tire safety when it actually does increase tire safety Stat211 Practice Exam 3 Final Exam d the quality assurance specialist decides that the new rubber compound has beneficial effects on tire safety when it actually does increase tire safety e none of the above 17 A manufacturer of automobile tires believes that a new rubber compound will increase the safety of the tires A quality assurance specialist must decide between the null hypothesis The new rubber compound has no beneficial effects on tire safety and the alternate hypothesis The new rubber compound increases tire safety A type 11 error would occur if a the quality assurance specialist decides that the new rubber compound has no beneficial effects on tire safety when it actually does not have any beneficial effects b the quality assurance specialist decides that the new rubber compound does increase tire safety when it actually does not have any beneficial effects c the quality assurance specialist decides that the new rubber compound has no beneficial effects on tire safety when it actually does increase tire safety d the quality assurance specialist decides that the new rubber compound has beneficial effects on tire safety when it actually does increase tire safety e none of the above 18 A vice president at a bank states that customers obtain service within an average time of 49 minutes of arriving at the bank s drive up service window However a long time customer of the bank wants to test the hypothesis that the average time to obtain service exceeds 49 minutes The customer collects data from 16 randomly selected customers and calculates the average time to obtain service The sample mean time is 53 minutes and the sample standard deviation is 12 minutes The alternate hypothesis would be a H A u gt 53 b 171A u lt 49 c HA u 49 d H A u 53 e H A u gt 49 19 A vice president at a bank states that customers obtain service within an average time of 49 minutes of arriving at the bank s drive up service window However a long time customer of the bank wants to test the hypothesis that the average time to obtain service exceeds 49 minutes The customer collects data from 16 randomly selected customers and calculates the average time to obtain service The sample mean time is 53 minutes and the sample standard deviation is 12 minutes The value of the test statistic rounded to the nearest hundredth is a 533 b 533 d 133 e cannot be determined with the information provided Stat211 Practice Exam 3 Final Exam 20 A vice president at a bank states that customers obtain service within an average time of 49 minutes of arriving at the bank s drive up service window However a long time customer of the bank wants to test the hypothesis that the average time to obtain service exceeds 49 minutes The customer collects data from 16 randomly selected customers and calculates the average time to obtain service The sample mean time is 53 minutes and the sample standard deviation is 12 minutes Suppose that the value of the test statistic is 146 Then the p value of the test statistic is a 09279 b 00721 c between 005 and 010 d cannot be determined with the information provided e none of the above 21 A vice president at a bank states that customers obtain service within an average time of 49 minutes of arriving at the bank s drive up service window However a long time customer of the bank wants to test the hypothesis that the average time to obtain service exceeds 49 minutes using a significance level of OL 001 The customer collects data from 16 randomly selected customers and calculates the average time to obtain service The sample mean time is 53 minutes and the sample standard deviation is 12 minutes If the researcher decides to reject the null hypothesis the researcher would conclude that a at the 1 significance level the average waiting time for these 16 bank customers to receive service does not exceed 49 minutes b at the 1 significance level the average waiting time for these 16 bank customers to receive service does exceed 49 minutes c at the 1 significance level the average waiting time for all of the bank customers to receive service does not exceed 49 minutes d at the 1 significance level the average waiting time for all of the bank customers to receive service does exceed 49 minutes e none of the above 22 Scores on the math section of a college entrance exam are normally distributed with a mean M 224 and standard deviation 031 Find the probability that a randomly selected test taker will score 25 or less on the math section of this exam a 07995 b 02005 c 08387 d 01613 e none of the above 23 Each person in a random sample of 200 voters was asked hisher opinion about the governor s proposed legislation and where the voter lives The data is given in the following table Stat211 Practice Exam 3 Final Exam Location A researcher wants to perform a hypothesis test in order to determine if the voter s location and hisher opinion are independent using a significance level of 005The expected value for the upper left cell E11 is a 50 b 54 c 70 d 66 e none of the above 24 Each person in a random sample of 200 voters was asked hisher opinion about the governor s proposed legislation and where the voter lives The data is given in the following table Location A researcher wants to perform a hypothesis test in order to determine if the voter s location and hisher opinion are independent using a significance level of 005 The number of degrees of freedom is 25 Each person in a random sample of 200 voters was asked hisher opinion about the governor s proposed legislation and where the voter lives The data is given in the following table Location A researcher wants to perform a hypothesis test in order to determine if the voter s location and hisher opinion are independent using a significance level of 005 Suppose Stat211 Practice Exam 3 Final Exam that the researcher fails to reject the null hypothesis Then the researcher would state hisher conclusion as a at the 5 significance level voter location and voter opinion are independent of each other b at the 5 significance level voter location and voter opinion are not independent of each other c at the 5 significance level rural voters tend to oppose the governors proposed legislation d at the 5 significance level urban voters tend to favor the governors proposed legislation e none of the above 26 Twenty eight percent of college freshmen do not return to college for their sophomore year of study A random sample of 12 college freshmen is obtained The probability that exactly two of the 12 freshmen will not return for their sophomore year is a 00784 b 00152 c 02528 d 01937 e none of the above 27 The GPAs of 31 randomly selected fraternity members and 36 randomly selected non fraternity students were obtained from the student body The sample mean and sample deviation for each sample are given in the table below Sample Observations Mean Std Dev Fraternity Members Sample X 31 203 068 Non Fraternity Students Sample Y 36 231 079 To determine if there is a difference between the average GPA of fraternity members and the average GPA of non fraternity students which set of hypotheses would be appropriate a H0 Mx My 0 HA Mx Mylt 0 b1710 Md 0 HA Md 0 c H0 Mx My 0 171A MX Mygt 0 d HO MX My 2 0 171A MX My 0 e none of the above 28 The GPAs of 31 randomly selected fraternity members and 36 randomly selected non fraternity students were obtained from the student body The sample mean and sample deviation for each sample are given in the table below Stat211 Practice Exam 3 Final Exam Sample Observations Mean Std Dev Fraternity Members Sample X 31 203 0 68 Non Fraternity Students Sample Y 36 231 079 The researcher wants to determine if there is a difference between the average GPA of fraternity members and the average GPA of non fraternity students Suppose that the value of the test statistic rounded to the nearest hundredth is 156 The p value of the test statistic is a 00594 b 01188 0 between 005 and 010 d 09406 e cannot be determined from the information provided 29 The GPAs of 31 randomly selected fraternity members and 36 randomly selected non fraternity students were obtained from the student body The sample mean and sample deviation for each sample are given in the table below Sample Observations Mean Std Dev Fraternity Members Sample X 31 203 068 Non Fraternity Students Sample Y 36 231 079 The researcher wants to determine if there is a difference between the average GPA of fraternity members and the average GPA of non fraternity students using a significance level of OL005 Suppose that the researcher decided to reject the null hypothesis Then the researcher would state hisher conclusion as a at the 5 significance level there does not seem to be a significant difference between the average GPA of fraternity members and the average GPA of non fraternity students b at the 5 significance level there does seem to be a significant difference between the average GPA of fraternity members and the average GPA of non fraternity students 0 at the 5 significance level the average GPA of fraternity members seems to be significantly higher than the average GPA of non fraternity students d at the 5 significance level the average GPA of fraternity members seems to be significantly lower than the average GPA of non fraternity students e none of the above 30 In a test of hypothesis the alternate hypothesis a is sometimes called the research hypothesis b is sometimes called the non research hypothesis 0 is sometimes called the null hypothesis d parts b and c only e none of the above 31 An event Stat211 Practice Exam 3 Final Exam a may consist of a single trial or a series of trials b is a set of outcomes with some common characteristic c is a subset of the sample space d parts b and c only e none of the above 32 The Council on Drug Abuse states that approximately 40 of college students have used at least one illegal drug However a sociology professor at ABC University wants to show that the percentage of students at ABC University who have used at least one illegal drug is less than 40 In a random sample of 100 students 47 state that they have used at least one illegal drug A hypothesis test is performed in order to determine if the data supports the claim of the sociology professor The alternate hypothesis would be a H A p 047 b H A p lt 040 c HA p 040 d H A u gt 040 e H A p lt 047 33 The Council on Drug Abuse states that approximately 40 of college students have used at least one illegal drug However a sociology professor at ABC University wants to show that the percentage of students at ABC University who have used at least one illegal drug is less than 40 In a random sample of 100 students 47 state that they have used at least one illegal drug A hypothesis test is performed in order to determine if the data supports the claim of the sociology professor Suppose that the value of the test statistic is 132 Then the p value of the test statistic is 34 The Council on Drug Abuse states that approximately 40 of college students have used at least one illegal drug However a sociology professor at ABC University wants to show that the percentage of students at ABC University who have used at least one illegal drug is less than 40 In a random sample of 100 students 47 state that they have used at least one illegal drug A hypothesis test is performed in order to determine if the data supports the claim of the sociology professor using a significance level of 010 If the researcher decides not to reject the null hypothesis the researcher would conclude that a at the 10 significance level more than 40 of students at ABC University have used at least one illegal drug b at the 10 significance level less than 40 of students at ABC University have used at least one illegal drug c at the 10 significance level approximately 40 of students at ABC University have not used any illegal drug d at the 10 significance level approximately 40 of students at ABC University have used at least one illegal drug Stat211 Practice Exam 3 Final Exam e none of the above 35 For the variables Xamount of time student studied for exam in hours and Y student score on exam suppose that a regression equation relating these variables is Y20 11 X Then the value 11 a represents the average score of all students b represents the average score of all students who did not study for the exam 0 has no meaningful interpretation d represents the average increase in exam score for every hour a student studied e none of the above 36 A group of 10 men were given a special diet for two weeks to test weight loss in pounds The observed data was Man Weight Before Diet Weight After Diet 1 178 2 171 172 3 190 185 4 187 184 5 210 201 6 202 201 7 166 160 8 173 168 9 183 180 10 184 179 To determine if the data provide sufficient evidence to indicate the special diet leads to a weight loss the appropriate test procedure is a two sample Z test b paired T test c paired Z test d two sample T test e none of the above 37 One thousand grapes are in a paper sack and have characteristics described in the table below I GRAPES I seedless I seeds I red 340 250 white 260 150 The probability that a randomly selected grape will be white and have seeds is a 0660 b 0164 c 0150 d 0164 e none of the above Stat211 Practice Exam 3 Final Exam 38 A researcher performed a hypothesis test in which she tested the null hypothesis H0 u 123 against the alternate hypothesis HA u 123 using a 10 significance level The researcher decided not to reject the null hypothesis Suppose the researcher constructs a 90 confidence interval on u The 90 confidence interval a would contain the value 123 b would not contain the value 123 c cannot be constructed after the researcher has performed a hypothesis test d there is insufficient information to say anything about the 90 confidence interval e none of the above 39 The sampling distribution of the sample mean a describes the distribution of the possible values that the sample mean may have for a sample of size n b describes the exact value of the sample mean for a sample of size n c describes the exact value of the population mean for a sample of size n d describes the value of the sample standard deviation for a sample of size n e none of the above 40 For a specific sample consisting of n observations the width of a 90 confidence interval on u a would be larger than the width of a 95 confidence interval on u b would be smaller than the width of a 95 confidence interval on u c would be the same as the width of a 95 confidence interval on u d cannot be compared to the width of a 95 confidence interval on u e none of the above

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