Statistics Questions

An experiment is run The mass of an object is recorded over time Time min 14 17 19 24 30 Plot the points in the grid below 50 45 40 35 30 25 20 15 10 Mass g 26 25 16 14 12 5 5 10 15 20 25 30 35 40 45 50 Clear All Draw Dot Using your calculator run a linear regression to determine the equation of t

A B AB O Total Rh Negative 45 73 22 49 189 Rh Positive 81 56 8 28 173 Total 126 129 30 77 362 Find the probability of choosing a donor with type A or Rh Negative blood Round to four decimals as needed Provide your answer below

Create Scatterplots for each of the tables of data below using your graphing calculator Determine which of the graphs most closely matches each table Then decide which table is Least Linear Moderately Linear and Most Linear Matching Graph Behavior Select an answer Least Linear Moderately Linear Most Linear Matching Graph Behavior Select an answer C Matching Graph Behavior Select an answer X f x 500 11939 12706 13998 540 580 620 14597 660 15779 700 16739 X f x 500 189 540 573 580 1213 620 2109 660 2739 700 4669 X 500 540 580 620 660 700 f x 5939 4172 8279 4796 7859 8339 A B C

9 Number of miles 20 9 18 12 10 17 14 13 14 14 15 11 Send data to calculator 17 3 a Complete the grouped frequency distribution for b Using the classes from part a draw the frequency the data Note that the class width is 5 polygon for the data Note that you can add or remove classes from the figure Label each class with its midpoint 0 5 to 5 5 Number of miles 5 5 to 10 5 10 5 to 15 5 15 5 to 20 5 X Frequency S Frequency 6 Number of miles

Anty 2300 dollars for Starbucks Over the course of one year she found that Apple went down 3 percent Google went up 4 percent and Starbucks went up 2 percent What is the average change in her portfolio Average change I percent

107 98 116 Temperatures in F 118 106 111 102 105 112 101 99 105 114 110 109 113 115 95 Send data to calculator a Complete the grouped frequency distribution for the data Note that the class width is 6 Temperatures in F 94 5 to 100 5 100 5 to 106 5 106 5 to 112 5 112 5 to 118 5 X Frequency 0 b Using the classes from part a draw the frequency polygon for the data Note that you can add or remove classes from the figure Label each class with its midpoint Frequency 6 5 4 3 2 0 Temperatures in F

A BCC professor decides to grade his class as following 20 percent for homework assignments 15 percent for quizzes 30 percent for a midterm and 35 percent for the final exam A student receives 81 for homework 86 for the quizzes 76 for the midterm and 95 for the final exam What will be the student s class grade Class grade

mm mm Round to two decimal places as needed Points 0 of 3 Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures Listed below are the widths mm of skulls from 150 A D Construct a 90 confidence interval estimate of the mean skull width 127 8 137 8 126 4 131 6 142 8 134 8 138 6 128 9 COST Save

Part 1 of 3 Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of 1 1 kg and a standard deviation of o 4 5 kg Complete parts a through c below a If 1 male college student is randomly selected find the probability that he gains between 0 kg and 3 kg during freshman year The probability is Round to four decimal places as needed

Points 0 of 3 A genetic experiment with peas resulted in one sample of offspring that consisted of 429 green peas and 152 yellow peas a Construct a 90 confidence interval to estimate of the percentage of yellow peas b Based on the confidence interval do the results of the experiment appear to contradict the expectation that 25 of the offspring peas would be yellow a Construct a 90 confidence interval Express the percentages in decimal form p Round to three decimal places as needed

Part 1 of 4 In a science fair project Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field She flipped a coin to select either her right hand or her left hand and then she asked the therapists to identify the selected hand by placing their hand just under Emily s hand without seeing it and without touching it Among 284 trials the touch therapists were correct 136 times Complete parts a through d COLO a Given that Emily used a coin toss to select either her right hand or her left hand what proportion of correct responses would be expected if the touch therapists made random guesses Type an integer or a decimal Do not round

When playing roulette at a casino a gambler is trying to decide whether to bet 5 on the number 13 or to bet 5 that the outcome is any one of the five possibilities 00 0 1 2 or 3 The gambler knows that the expected value of the 5 bet for a single number is 53 For the 5 bet that the outcome is 00 0 1 2 or 3 there is a probability of 5 of making a net profit of 25 and a probability of losing 5 33 38 38 a Find the expected value for the 5 bet that the outcome is 00 0 1 2 or 3 b Which bet is better a 5 bet on the number 13 or a 5 bet that the outcome is any one of the numbers 00 0 1 2 or 3 Why a The expected value is Round to the nearest cent as needed

CQ1 Construct a two way table with 100 women and 80 men in which both groups show equal percentages of right handedness

5 51 Independent Suppose a person is chosen at random Use your understanding about the world of basketball to decide whether the event that the person is taller than six feet and the event that the person plays professional basketball are independent or associated Explain

5 17 Birthdays What is the probability that a baby will be born on a Friday OR a Saturday OR a Sunday if all the days of the week are equally likely as birthdays

5 48 College Poll A person is selected randomly from the entire group whose responses are summarized in the table for Exercise 5 47 We want to find the probability that the person selected is a male who said yes Which of the following statements best describes the problem i P Yes Male ii P Malel Yes iii P Male AND Yes

5 8 Random Assignment of Professors A study randomly assigned students attending the Air Force Academy to different pro fessors for Calculus I with equal numbers of students assigned to each professor Some professors were experienced and some were relatively inexperienced Suppose the names of the professors are Peters Parker Diaz Nguyen and Black Suppose Diaz and Black are inexperienced and the others are experienced The researchers reported that the students who had the experienced teachers for Calculus I did better in Calculus II Source Scott E Carrell and James E West Does Professor Quality Matter Evidence from Random Assignment of Students to Professors 2010 a List the equally likely outcomes that could occur for assignment of one student to a professor b Suppose the event of interest event A is that a teacher is experienced List the outcomes that make up event A c What is the probability that a student will be assigned to an experienced teacher d List the outcomes in the complement of event A Describe this complement in words e What is the probability that a student will be assigned to an inexperienced teacher

5 14 Guessing on Tests Consider a multiple choice test with a total of four possible options for each question a What is the probability of guessing correctly on one question Assume that there are three incorrect options and one correct option b What is the probability that a guess on one question will be incorrect

5 7 Criminal Court Judges Criminal cases are assigned to judges andomly The list of the criminal judges for Memphis Tennessee taken from the Tennessee Court System website www tsc state tn us is given in the table Assume that only Carolyn Blackett and Paula Skahan are women and the rest are men If you were a criminal defense attorney in Memphis you might be interested in whether the udge assigned to your case was a man or a woman James C Beasley Carolyn W Blackett Lee V Coffee Chris Craft John T Fowlkes W Otis Higgs James M Lammey Paula L Skahan W Mark Ward

5 10 Which of the following numbers could not be probabilities and why a 125 b 0 74 c 0 001 d 5 61 e 150 TRY 5 11 Playing Cards Example 2 There are four suits clubs diamonds hearts and spades 4 and the following cards appear in each suit ace 2 3 4 5 6 7 8 9 10 jack queen king The jack queen and king are called face cards because they have a drawing of a face on them Diamonds and hearts are red and clubs and spades are black If you draw 1 card randomly from a standard 52 card playing deck what is the probability that it will be a A heart b A red card c An ace d A face card jack queen or king e A three 5 12 Playing Cards Refer to Exercise 5 11 for information about cards If you draw 1 card randomly from a standard 52 card playing deck what is the probability that it will be a A black card b A diamond c A face card jack queen or king d A nine e A king or queen 5 13 Guessing on Tests a On a true false quiz in which you are guessing what is the probability of guessing correctly on one question b What is the probability that a guess on one true false question will be incorrect 5 14 Guessing on Tests Consider a multiple choice test with a total of four possible options for each question a What is the probability of guessing correctly on one question Assume that there are three incorrect options and one correct option b What is the probability that a guess on one question will be incorrect TRY 5 15 Four Children Example 3 The sample space given here shows all possible sequences for a family with 4 children where B stands for boy and G stands for girl GGGG GGGB GGBB GBBB BBBB GGBG GBGB BGBB GBGG GBBG BBGB BGGG BGGB BBBG BGBG BBGG Assume that all of the 16 outcomes are equally likely Find the probability of having the following numbers of girls out of Hint The probability of having 3 girls and a boy is 4 16 or 25 because the second column shows that there are 4 ways to have 3 girls and I boy 5 16 Three Coins The sample shows the possible sequences for flipping three fair coins or flipping one coin three times where H stands for heads and T stands for tails HHH HHT HTH THH Assume that all of the 8 outcomes are equally likely Find the probability of having exactly the following numbers of heads out of the 3 coins a exactly 0 heads b exactly 1 head c exactly 2 heads d exactly 3 heads e What do the four probabilities add up to and why No HTT THT TTH 5 17 Birthdays What is the probability that a baby will be born on a Friday OR a Saturday OR a Sunday if all the days of the week are equally likely as birthdays 5 18 Playing Cards If one card is selected from a well shuffled deck of 52 cards what is the probability that the card will be a club OR a diamond OR a art What is probab of the complement of this event Refer to Exercise 5 11 for information about cards Unsure Yes TTT 5 19 College Poll A StatCrunch poll asked people if college was worth the financial investment They also asked the respondent s gender The table shows a summary of the responses Source StatCrunch Responses to Is college worth it Owner scsurvey All Female Male 45 56 100 96 577 401 722 553 All 101 196 978 1275 a If a person is chosen randomly from the group what is the probability that the person is male b If a person is chosen randomly from the group what is the probability that the person said Yes 5 20 College Poll Refer to the table given for Exercise 5 19 a If a person is chosen randomly what is the probability that the person is female b If a person is chosen randomly what is the probability that the person said No TRY 5 21 College Poll AND Example 4 Refer to the table given for Exercise 5 19 If a person is chosen randomly from the group what is the probability that the person is female AND said Yes 5 22 College Poll AND Refer to the table given for Exercise 5 19 If a person is chosen randomly from the group what is the probability that the person is male AND said No TRY 5 23 College Poll OR Example 5 Refer to the table given for Exercise 5 19 a If a person is chosen randomly from the group what is the probability

5 16 Three Coins The sample shows the possible sequences for flipping three fair coins or flipping one coin three times where H stands for heads and T stands for tails HHH HHT HTH THH HTT THT TTH TTT Assume that all of the 8 outcomes are equally likely Find the probability of having exactly the following numbers of heads out of the 3 coins a exactly 0 heads b exactly 1 head c exactly 2 heads d exactly 3 heads e What do the four probabilities add

a On a true false quiz in which you are guessing what is the probability of guessing correctly on one question b What is the probability that a guess on one true false question will be incorrect

5 1 Simulation Example 1 If we flip a coin 10 times how often do we get 6 or more heads A first step to answering this question would be to simulate 10 flips Use the random number table in Appendix A to simulate flipping a coin 10 times Let odd digits 1 3 5 7 9 represent heads and let even digits 0 2 4 6 8 represent tails Begin with the first digit in the third row a Write the sequence of 10 random digits b Write the sequence of 10 heads and tails Write H for heads and T for tails c How many heads did you get Did you get 6 or more heads

5 11 Playing Cards Example 2 There are four suits clubs diamonds hearts and spades and the following cards appear in each suit ace 2 3 4 5 6 7 8 9 10 jack queen king The jack queen and king are called face cards because they have a drawing of a face on them Diamonds and hearts are red and clubs and spades are black If you draw 1 card randomly from a standard 52 card playing deck what is the probability that it will be a A heart b A red card c An ace d A face card jack queen or king A throa

5 9 Which of the following numbers could not be probabilitie and why a 5 63 b 0 063 c 0 063 d 163 e 1 63

80 78 75 81 76 89 74 Test scores 82 85 Send data to calculator Test scores 71 5 to 75 5 75 5 to 79 5 79 5 to 83 5 a Complete the grouped frequency distribution for the data Note that the class width is 4 83 5 to 87 5 74 87 5 to 91 5 83 90 Frequency 73 88 0 0 0 82 79 b Using the classes from part a draw the frequency polygon for the data Note that you can add or remove classes from the figure Label each class with its midpoint Frequency 6 5 4 3 2 Test scores L

Over the years a sushi restaurant has had a mean customer satisfaction rating of 72 5 with a variance of 25 4 The owner wants to see if using a new menu will have any effect on the variance o The owner surveys a random sample of 14 customers who ordered from the new menu For the customers surveyed the variance of ratings is 46 2 Assume the ratings for customers who order from the new menu follow a normal distribution Is there enough evidence to conclude that the population variance differs from 25 4 To answer complete the parts below to perform a hypothesis test Use the 0 10 level of significance a State the null hypothesis H and the alternative hypothesis H that you would use for the test Ho H 0 0 S O O Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places Step 2 Select one tailed or two tailed O One tailed O Two tailed b Perform a chi square test and find the p value Here is some information to help you with your chi square test Step 5 Enter the p value Round to 3 decimal places X The value of the test statistic is given by x n 1 s G Step 4 Shade the area represented by the p value Osa The p value is two times the area under the curve to the right of the value of the test statistic 0 0 Since the O O 5 D 3 12 424 0 1 Yo Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance differs from 25 4 c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the population variance of ratings for customers who order from the new menu Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the variance differs from 25 4 Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance differs from 25 4 is ir greater than the lovel of X X S TERE A M

machine is properly calibrated its welds have a mean length of 22 00 mm with a standard deviation of 0 16 mm It has been a while since the machine has been serviced Because of this the foreman has told you to perform a hypothesis test to determine if the standard deviation G of the weld lengths is greater than when this machine is properly calibrated To do so you choose at random a sample of size 11 and examine the weld lengths You find they have a sample standard deviation of 0 21 mm Assume the weld lengths follow a normal distribution Is there enough evidence to conclude that the population standard deviation o is greater than 0 16 mm To answer complete the parts below to perform a hypothesis test Use the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis H that you would use for the test Ho O O O O 0 0 0 0 020 O O OSO b Perform a chi square test and find the p value Here is some information to help you with your chi square test Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places The value of the test statistic is given by n 1 s G S The p value is the area under the curve to the right of the value of the test statistic Step 2 Select one talled or two tailed O One tailed OTwo tailed Step 5 Enter the p value Round to 3 decimal places X Step 4 Shade the area represented by the p value 03 624 0 1 10 c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the population standard deviation in the weld lengths Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the standard deviation is greater than 0 16 mm Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the standard deviation is greater than 0 16 mm 20 Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the standard deviation is greater than 0 16 mm Since the p value is greater than the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the standard deviation is greater than 0 16 mm 30 X 14

According to past research plesterol levels of adult males are approximately normally distributed with a mean of 224 and a standard deviation of 21 7 Some researchers specializing in health care claim that because healthier foods have become more expensive the standard deviation o Of cholesterol levels of adult males is now less than 21 7 The researchers take a random sample of 21 adult males and measure their cholesterol levels The people in the sample have a mean cholesterol level of 225 5 and a standard deviation of 14 0 Is there enough evidence to conclude at the 0 10 level of significance that the standard deviation of cholesterol levels of adult males is now less than 21 7 a State the null hypothesis H and the alternative hypothesis H H H 0 Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places 0 mg dL d Find the critical value Round to three or more decimal places 0 e Can we support the claim that the standard deviation of cholesterol levels of adult males is now less than 21 7 3 XI mg dL a X S 2 0 0 OSO 0 0 O O P 010 20 O O

A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 2 9 hours with a standard deviation of 0 50 A government group conducts an independent study on the new pill to see if the standard deviation o of increase in sleeping time is higher than the advertised standard deviation The government group tests 10 insomniacs chosen at random with the new pill The insomniacs in the sample report a mean daily sleeping increase of 3 hours with a standard deviation of 0 65 Is there enough evidence at the 0 05 level of significance to support the claim that the standard deviation of increase in sleeping time is higher than the one advertised Assume that the increases in sleeping times provided by the new pill are approximately normally distributed Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H Ho H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the critical value Round to three or more decimal places 0 e Can we support the claim that the standard deviation of increase in sleeping time using the new pill is higher than the one advertised OYes No H XI 0 0 X O S Jn OSO 0 P Q 00 020 0

Tire lifetimes The lifetime of a certain type of automobile tire in thousands of miles is normally distributed with mean 40 and standard deviation o 6 Use the TI 84 Plus calculator to answer the following a Find the 12th percentile of the tire lifetimes b Find the 64th percentile of the tire lifetimes c Find the third quartile of the tire lifetimes d The tire company wants to guarantee that its tires will last at least a certain number of miles What number of miles in thousands should the company guarantee so that only 3 of the tires violate the guarantee Round the answers to at least two decimal places Part 1 of 4 The 12th percentile of the tire lifetimes is thousand miles X S

cire lifetimes is lifetimes is tee thousand miles thousand miles thousand miles X X X 5

Baby weights The weight of male babies less than 2 months old in the United States is normally distributed with mean 12 2 pounds and standard deviation 4 5 pounds Use Excel to answer the following Round the answers to four decimal places Part 0 4 Part 1 of 4 a What proportion of babies weigh more than 13 pounds The proportion of babies weighing more than 13 pounds is

A normal population has mean 39 and standard deviation o 10 a What proportion of the population is between 17 and 28 b What is the probability that a randomly chosen value will be between 35 and 45 Round the answers to at least four decimal places Part 1 of 2 The proportion of the population between 17 and 28 is Part 2 of 2 X The probability that a randomly chosen value will be between 35 and 45 is

A normal population has mean 10 and standard deviation o 7 a What proportion of the population is less than 18 b What is the probability that a randomly chosen value will be greater than 3 Round the answers to four decimal places Part 0 2 Part 1 of 2 The proportion of the population less than 18 is X

A normal population has mean 51 and standard deviation o 7 What is the 85th percentile of the population Use the TI 84 Plus calculator Round the answer to at least one decimal place The 85th percentile of the population is X

Part If two institutions have budgets that differ by 24 million dollars in 2006 by how much would you predict their budgets to differ in 2018 Round the answer to three decimal places In 2018 their budgets would differ by 24 2328 million dollars Part 2 3 Part 3 of 3 Predict the 2018 budget for an organization whose 2006 budget was 210 million dollars Round the answer to one decimal place The 2018 budget is predicted to be million dollars X

If the price of eggs differ by 0 35 from one month to the next by how much would you expect the price of milk to differ Round the answer to two decimal places The price of milk would differ by 0 08 Part 2 3 Part 3 of 3 Predict the price of milk in a month when the price of eggs is 2 20 Round the answer to two decimal places The price of milk is predicted to be X S

and data to Excel Part 1 of 3 Compute the least squares regression line for predicting the 2018 budget y from the 2006 budget x Round the slope and y intercept to at least four decimal places Regression line equation y 1 0097x 4 1944 Part 1 3 Part 2 of 3 If two institutions have budgets that differ by 24 million dollars in 2006 by how much would you predict their budgets to differ in 2018 Round the answer to three decimal places In 2018 their budgets would differ by million dollars Espa ol 8E 20

Based on results published in the Journal of Human Hypertension Send data to Excel Part 1 of 4 Compute the least squares regression line for predicting the diastolic pressure y from the systolic pressure x Round the slope and y intercept to at least four decimal places Regression line equation y 0 59136x 8 26713 Part 1 4 Part 2 of 4 Is it possible to interpret the y intercept Explain

has been serviced Because of this the foreman has told you to perform a hypothesis test to determine if the standard deviation G of the weld lengths is greater than when this machine is properly calibrated To do so you choose at random a sample of size 11 and examine the weld lengths You find they have a sample standard deviation of 0 21 mm Assume the weld lengths follow a normal distribution Is there enough evidence to conclude that the population standard deviation o is greater than 0 16 mm To answer complete the parts below to perform a hypothesis test Use the 0 05 level of significance a State the null hypothesis H and the alternative hypothesis that you would use for the test 0 S 0 0 OSO Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places 020 Step 2 Select one tailed or two tailed O One tailed O Two tailed Step 5 Enter the p value Round to 3 decimal places b Perform a chi square test and find the p value Here is some information to help you with your chi square test The value of the test statistic is given by 1 The p value is the area under the curve to the right of the value of the test statistic Step 4 Shade the area represented by the p value X 0 0 0 0 O O 03 4 2 E 10 Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the standard deviation is greater than 0 16 mm Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the standard deviation is greater than 0 16 mm Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the standard deviation is greater than 0 16 mm 20 c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the population standard deviation in the weld lengths Since the p value is greater than the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the standard deviation is greater than 0 16 mm 25 30 X X 5 35 S A M

funding The following table presents the budget in millions of dollars for selected organizations that received U S government funding for arts and culture in both 2006 and 2018 Organization National Endowment for the Humanities National Endowment for Arts National Gallery of Art Kennedy Center for the Performing Arts Smithsonian Institution Corporation for Public Broadcasting Institute of Museum and Library Services Send data to Excel Part 0 3 Part 1 of 3 2006 135 121 88 17 8 4 4 2018 142 124 95 18 2 5 24 Compute the least squares regression line for predicting the 2018 budget y from the 2006 budget r Bound the slone and win langt four

b Compute the correlation coefficient between systolic and diastolic blood pressure Round the answer to at least three decimal places The correlation coefficient is r 0 8605 Part 2 3 Part 3 of 3 X c If someone s diastolic pressure is above average would you expect that person s systolic pressure to be above or below average Explain I would expect the person s systolic pressure to be Choose one average since r is positive positive negative

174 000 This process includes only the cost of processing the claim payments not the actual amount of the claim payments The adjusting activity involves verifying and estimating the amount of the claim and is variable to the number of claims adjusted The process received adjusted and paid 5 800 claims during the period All claims were treated identically in this process To improve the cost of this process management has determined that claims should be segregated into two categories Claims under 1 000 and claims greater than 1 000 claims under 1 000 would not be adjusted but would be accepted upon the insured s evidence of claim Claims above 1 000 would be adjusted It is estimated that 65 of the claims are under 1 000 and would thus be paid without adjustment It is also estimated that the additional effort to segregate claims would add 5 to the receiving claim activity cost Total a Develop a table showing the percent of individual activity cost to the total process cost Round the percents to the nearest whole number if required Statewide Insurance Company Individual activity cost to the total process cost Activities Activity Cost Receiving claim Adjusting claim Percent of Total Process

Great Pumpkins When growing giant pumpkins for competitions growers need to keep track of the weights of the pumpkins while they are growing It is difficult to weigh a large pumpkin before it is harvested so a method has been developed for estimating the weight The grower measures around the pumpkin both horizontally and vertically then adds the results This is called the OTT over the top measurement and is used to predict the weight of the pumpkin Following are the OTT measurements and actual weights of the 10 largest pumpkins entered into official competitions in a recent year OTT inches 454 0 454 0 463 0 469 0 465 0 456 0 457 0 455 0 477 0 456 0 Send data to Excel Weight pounds 2020 5 2138 9 2170 0 2469 0 2138 0 2091 0 2079 0 2283 0 2157 5 2077 0

Age discrimination The following table presents the numbers of employees by age group who were promoted or not promoted in a sample drawn from a certain industry during the past year Promoted Not promoted Send data to Excel Under 30 17 48 30 39 31 48 Age 40 49 20 51 50 and Over 22 Time Remaining 1 46 05 47 Can you conclude that the people in some age groups are more likely to be promoted than those in other age groups Use Excel and the a 0 10 level of significance We Choose one the null hypothesis There Choose one enough evidence at the a 0 10 level of significance to say that people in some age groups are more likely to be promoted Ella Esp C

insomniacs by an average of 2 7 hours with a variance of 0 30 A governr group conducts an independent study on the new pill to see if the varianc of increase in sleeping time is different from the advertised variance The government group tests 23 insomniacs chosen at random with the nev The insomniacs in the sample report a mean daily sleeping increase of hours with a variance of 0 58 Is there enough evidence at the 0 05 leve significance to reject the claim made in the advertisement Assume th the increases in sleeping times provided by the new pill are approxima normally distributed Perform a two tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H HO H b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the two critical values Round to three or more decimal places and e Can we reject the claim that the variance of increase in sleeping time using the new pill is as advertised OYes No H x X 0 a X S 0 0 OSO 020 P 0 0 00 0

A Pr A is closest to 03 14 07 15 03 5 07 17 011 16 011 14 07 12 07 19 Pr B is closest to 08 12 03 5 011 16 07 14 07 17 07 19 6 15 PrA U B is closest to 09 12 14 14 15 16 3 5 B C

new menu will have any effect on the variance The owner surveys a random sample of 19 customers who ordered from the new menu For the customers surveyed the variance of ratings is 13 9 Assume the ratings for customers who order from the new menu follow a normal distribution Is there enough evidence to conclude that the population variance differs from 25 6 To answer complete the parts below to perform a hypothesis test Use the 0 10 level of significance a State the null hypothesis and the alternative hypothesis that you would use for the test Ho H 0 Chi square Distribution O Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places O 0 0 0 O O Step 2 Select one tailed or two tailed O One tailed OTwo tailed Step 5 Enter the p value Round to 3 decimal places 0 20 0 0 b Perform a chi square test and find the p value Here is some information to help you with your chi square test The value of the test statistic is given by 1 s The p value is two times the area under the curve to the left of the value of the test statistic S Step 4 Shade the area represented by the p value X 0 03 02 1 10 Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance differs from 25 6 c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the population variance of ratings for customers who order from the new menu Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the variance differs from 25 6 Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance differs from 25 6 Since the p value is greater than the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the variance differs from 25 6 30 X X 3 O BEEN Aa M

Consider the scotterplot 1400 COOL 600 test net vol vs effectiveness 15 10 5 0 5 effectiveness 10 15 20 The correlation coefficient between effectiveness and test net vol is closest to 0 04749 0 97918 0 69359 0 41733 0 97902 0 70349 The regression line slope between effectiveness and test net vol is closest to D 78 28817 0 13977 6 96502 39 27934 8 42833 The regression line y intercept is closest to 4199 71609 404 18811