Statistics Questions

Q36 Let h x x 2 g x sin x 3 then find the value of goh 2 hog 2 a b sin 2 1 2 sin 4 1 2 c sin 2 1 2 d sin 2 1

Question 5 Mandatory 4 points A 12 sided die can be made from a geometric solid called a dodecahedron Assume that a fair dodecahedron is rolled The sample space is 1 2 3 4 5 6 7 8 9 10 11 12 Find P Greater than 8 1 4 1 3 1 12

Vang Enterprises estimates that its WACC is 10 20 The company is considering the follwoing 7 capital budgeting projects in millions Project 1 234567 6 70 7 Assume that each of these projects is just as risky as the firm s existing assets Its CFO hired you to assist in deciding whether none some or all of the projects should be accepted If these are the only projects under consideration how large should the capital budget be O 102 80 172 Rate of Return Size millions 13 00 10 90 10 80 10 40 10 10 9 15 7 60 137 28 00 25 00 27 00 22 00 25 00 23 00 22 00

A normal distribution has a mean of u 40 with d 10 If a vertical line is drawn through the distribution at X 34 which proportion of the scores are on the left side of the line 0 7257 0 2743 0 0668 0 1976

b Does the residual plot indicate that a linear model for the x y data is appropriate Also explain why Linear regression vimbe 23 462 0 7755 Finall 134 enky s 10 00 2 RAG 0 1421 ANJANG AKLE 4 04

8 10 a Does the residual plot indicate that a linear model for the x y data is appropriate Also explain why Residual 0 6 10 15 Residuals Versus the Fitted Values response is strength 20

set Select the table copy then Edit Paste Special Paste Values Only 14 6 15 9 20 6 29 4 31 4 35 41 5 47 7 22 7 26 3 23 43 2 26 7 40 7 38 42 4 39 8 25 1 45 22 4 28 8 38 32 2 30 4 26 3 22 7 15 35 9 30 34 4 24 9 33 7 34 7 42 4 24 6 23 8 29 30 27 3 34 4 21 7 18 8 28 6 29 6 31 6 34 9 35 9 13 6 34 7 24 9 11 4 39 21 34 20 6 32 9 33 5 37 31 18 8 37 46 4 29 2 19 3 28 6 39 8 23 3 11 4 32 2 30 4 What is the mean of this data set mean 29 41 X Report answer to 2 decimal places What is the median of this data set median 30 Report answer to 2 decimal places What is the maximum of this data set max 47 7 What is the minimum of this data set min 8 OF X What is the mid range of this data set

5 The following data show salaries y and the grade point averages z for students who obtained a bachelor s degree in Economics The estimated regression equation for these data is 1790 5 581 1z Show steps when applicable I 2 6 3 4 3 6 3 2 3 5 2 9 y 3300 3600 4000 3500 3900 3600 a When no information for GPA is given the estimate of salary is b In the given data how much is the estimated error when the GPA is 2 9 c If Jim has a perfect GPA 4 0 how much salary can he expect d If Jack increases his GPA by 1 0 how much more salary can he expect

A pet association claims that the mean annual cost of food for dogs and cats are the same The results for samples for the two types of pets are shown below At 0 05 can you reject the pet association s claim Assume the population variances are not equal Assume the samples are random and independent and the populations are normally distributed Complete parts a through e below Dogs X1 219 S 42 n 17 Cats X2 184 a Identify the claim and state Ho and Ha Which is the correct claim below OA The mean annual cost of food for dogs is greater than the cost for cats B The mean annual costs of food for dogs and cats are not equal OC The mean annual cost of food for cats greater than the cost for dogs D The mean annual costs of food for dogs and cats are equal What are Ho and Ha The null hypothesis Ho is The alternative hypothesis Ha is M Which hypothesis is the claim The null hypothesis Ho The alternative hypothesis Ha S2 38 n 14 b Find the critical value s and identify the rejection region s Enter the critical value s below O A t to B t to t to C to t to Type an integer or decimal rounded to three decimal places as needed Use a comma to separate answers as needed Select the correct rejection region s below O D t to c Find the standardized test statistic t Type an integer or decimal rounded to three decimal places as needed d Decide whether to reject or fail to reject the null hypothesis the null hypothesis e Interpret the decision in the context of the original claim

Complete parts a through h for the data below 70 80 46 33 X 40 y 63 90 30 0 50 58 60 53 100 G 100 04 30 x 90 100 M 04 30 d By hand determine the least squares regression line y 0 72 x 93 8 Round to three decimal places as needed e Graph the least squares regression line on the scatter diagram Choose the correct graph below x 90 Q 90 30 30 90 O G L

In a national survey college students were asked How often do you wear a seat belt when riding in a car driven by someone else The response frequencies appear in the table to the right a Construct a probability model for seat belt use by a passenger b Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else a Complete the table below Response Never Probability Round to the nearest thousandth as needed Response Never Rarely Sometimes Most of the time Always Frequency 121 309 509 1356 2426

The table shows the results of rolling a fair six sided die Complete parts a through d below Outcome on 100 Die Trials 1 18 2 15 3 456 15 21 16 15 100 Trials 500 Trials 15 82 13 92 79 78 85 84 20 15 23 a Using the table find the empirical probability of rolling a 2 for the first 100 trials The empirical probability of rolling a 2 for the first 100 trials is Round to two decimal places as needed

Complete parts a through h for the data below 70 80 C 46 33 X 40 y 63 0 30 50 60 58 53 The line in part X 90 0 30 90 30 0 100 f Compute the sum of the squared residuals for the line found in part b 44 000 Round to three decimal places as needed g Compute the sum of the squared residuals for the least squares regression line found in part d 26 8 Round to three decimal places as needed h Comment on the fit of the line found in part b versus the least squares regression line found in part d passes through the most points The line in part WITH 30 30 90 the sum of the squared residuals thus being the best fitting line

1 Let T be a random variable that follows the Students t distribution with 11 degrees of freedom Use the t chart to approximate P T 1 363 Note If you do not use the t chart you will need to round your answer to the nearest hundredths Answer Continue Reset answer

In an effort to gauge how the country s population feels about the immigration researchers surveyed adult citizens One question asked was On the whole do you think immigration is a good thing or a bad thing for this country today The results of the survey by ethnicity are given in the acompanying table Complete parts a through f Click the icon to view the data table Opinion Ethnicity Blacks Hispanics marginal distribution Non Hispanic Whites Good thing Bad thing Good and bad No opinion Relative frequency marginal distribution Pound to three decimal places as needed 185 107 9 9 152 105 14 11 144 33 12 6 Relative frequ Data table Good thing Bad thing Good and bad No opinion Non Hispanic Whites 185 1 07 9 9 Print Blacks 152 105 14 11 Done Hispanics 144 33 6

A professor feels that there is a relation between the number of hours a statistics student studies each week and the student s age She conducts a survey in which 26 statistics students are asked their age and the number of hours they study statistics each week She obtains the accompanying results Complete parts a through e Click the icon to view the data table OB 18 1 1 C 35 8 3 XD There are no potential influential observations b Find the least squares regression line using all the data poin y 0 239 x 1 07 Round the splope to three decimal places as needed Round th c Find the least squares regression line with the data point 34 y x X Round the splope to three decimal places as needed Round th Data table Age x 18 18 18 18 89 890 0 18 18 19 19 19 Hours Studying y 4 2 21 1 1 435 3 2 23 22832 4 6 61 3 1 5 2 3 2 2 8 2 3 3 2 Age x 19 19 20 20 20 20 21 21 21 Hours Studying y 5 1 2 3 1 7 635 NO 6 2 3 2 5 3 2 5 6 4 4 2 Age x 22222285 24 26 26 35 Hours Studying y 2 1 w NN o A SEN 3 6 5 3 4 8 3 9 5 2 4 2 8 3 C

In N 25 games last season the college basketball team averaged 83 points with a standard deviation of d 8 In their final game of the season the team scored 78 points Based on this information the number of points scored in the final game was a little above average far below average a little below average There is not enough information provided to know

Consider the data set given in the accompanying table Complete parts a through d Click the icon to view the data table Y 50 30 Y Y2 25 25 80 Y2 Marginal distribution b Construct a relative frequency marginal distribution 50 30 50 X1 50 30 80 X2 25 25 105 105 Relative frequency marginal distribution Round to three decimal places as needed 210 X3 30 50 Relative frequency marginal distribution 1 Data table Y Y2 Print X 50 30 X 25 25 X3 30 50 Done 0 I

professor feels that there is a relation between the number of hours a statistics student studies each week and the student s age She conducts a survey in which 26 statistics students are asked their age and the number of hours they study statistics each week She obtains the accompanying results Complete parts a through e Click the icon to view the data table Study Time 18 00 27 36 Age Q 1 Study Time 18 27 Age 36 Q 5 Determine any potential influential observations Choose the correct answer below A 20 6 2 and 21 6 4 B 18 1 1 C 35 8 3 XD There are no potential influential observations d b Find the least squares regression line using all the data points Choose the correct answer below y x Round the splope to three decimal places as needed Round the intercept to two decimal places as needed www Study Time Data table Age x 18 18 18 18 18 18 19 19 19 Hours Studying y 4 2 1 1 46 3 1 5 2 3 2 2 8 2 3 3 2 30 Age x 19 19 20 20 20 20 21 21 21 Print Hours Studying y 5 1 2 3 1 7 6 2 3 2 5 3 2 5 6 4 4 2 Done Hours Age x Studying y 2 1 3 6 5 3 4 8 25 3 9 5 2 42 8 3 222242LS 25 26 26 35 X

29 7 32 9 35 9 43 47 7 50 5 56 3 63 8 36 4 41 51 5 55 7 60 36 7 45 4 51 2 47 7 44 2 41 5 38 8 45 4 43 8 42 6 60 45 8 37 4 44 4 34 3 52 3 34 7 31 8 38 8 39 9 50 9 54 38 3 32 6 34 3 52 6 36 7 33 8 51 5 38 3 48 7 49 4 41 9 45 4 49 7 58 2 46 33 2 41 7 48 7 35 6 46 6 61 4 38 5 44 6 46 2 49 9 41 56 2 32 6 46 6 37 7 49 7 47 57 4 41 7 47 7 What is the mean of this data set mean 44 6 Report answer to 2 decimal places What is the median of this data set median 45 4 X Report answer to 2 decimal places What is the maximum of this data set max 63 8 What is the minimum of this data set min 29 7 OF What is the mid range of this data set mid range 46 75

The following data represent the high temperature distribution for a summer month in a city for some of the last 130 years Treat the data as a population Complete parts a through c Temperature Days 50 59 5 60 69 321 b Use the frequency histogram of the data to verify that the distribution is bell shaped O No the frequency histogram of the data is not bell shaped n Yes the frequency histogram of the data is bell shaped 1700 0 and HA ono decimal place as needed Use ascending order 50 70 79 1459 110 c According to the empirical rule 95 of days in the month will be between what two temperatures 80 89 1512 90 99 446 100 109 8

histogram depicts a higher standard deviation Frequency 10 8 6 4 2 0 30 40 Choose the correct answer below 50 601 70 a OA Histogram a depicts the higher standard deviation since it is more bell shaped CER Aouanbe OD OC Histogram b depicts the higher standard deviation because the bars are higher than the average bar in a 10 8 6 2 0 40 44 Th 48 52 56 60 b OB Histogram b depicts the higher standard deviation because the distribution has more dispersion Histogram a depicts the higher standard deviation because the distribution has more dispersion

The following data represent the weight in grams of a random sample of 13 medicine tablets Find the five number 0 599 0 600 0 598 0 599 summary and construct a boxplot for the data Comment on the shape of the distribution 0 600 0 602 0 604 0 600 0 598 0 611 0 604 0 601 0 606 TTTT 0 6 0 61 0 6 0 61 Choose the correct description of the shape of the distribution OA The distribution is roughly symmetrical OB The distribution is skewed to the right OC The distribution is skewed to the left D The shape of the distribution cannot be determined from the boxplot G 0 6 0 61

The following data represent the dividend yields in percent of a random sample of 28 publicly traded stocks Complete parts a to c 0 1 2 3 0 c Determine the shape of the distribution from the boxplot OA The distribution is roughly symmetric OB The distribution is skewed to the right OC The distribution is skewed to the left 1 2 13 of the distribution cannot be determined from the boxplot 4 1 25 1 25 0 39 0 48 possible 0 39 1 13 0 22 0 82 1 33 0 27 0 0 38 0 53 2 28 1 35 1 49 3 44 1 79 0 0 84 72 2 79 2 01 2 87 0 48 3 2 0 0 1 52

Approximate the mean for following GFDT Data Frequency 30 34 1 35 39 1 40 44 4 45 49 6 50 54 7 55 59 9 60 64 12 65 69 22 70 74 13 mean

The examinations in a large accounting class are scaled after grading so that the mean score is 50 The professor thinks that one teaching assistant is a poor teacher and suspects that his students have a lower mean score than the class as a whole The TA s students this semester can be considered a random sample from the population of all students in the course so the professor compares their mean score with 50 State the hypotheses Ho and Ha a Ho 50 Ha 50 b Ho 50 H the sample s mean a c Ho 50 Ha 50 d Ho 50 Ha 50

A cellular phone company monitors monthly phone usage The following data represent the monthly phone use in minutes of one particular customer for the past 20 months Use the given data to answer parts a and b and the interquartile range What property does this illustrate Choose the correct answer below a Determine the standard deviation and interquartile range of the data S Round to two decimal places as needed IQR Type an integer or a decimal b Suppose the month in which the customer used 325 minutes was not actually that customer s phone That particular month the customer did not use their phone at all so 0 minutes were used How does changing the observation from 325 to 0 affect the standard deviation and interquartile range What property does this illustrate The standard deviation Empirical Rule 325 433 402 347 416 478 380 333 445 409 531 550 410 406 336 476 524 546 394 431

1 50 FUAYEN P PAR HOT 1 25 1 00 1 00 con TERHENT IN THE MEKAHE JANNE S DAMES MEE TE Omina da PENPUTERIN SHENTREN TREE A HENSILA SHAPERS LEI BERGE NUAN N 154 For a population with u 84 and 0 4 what is the z score corresponding to X 80 SENTEN DEZEA5 THEN TEINE Nemme mes THE CENT TUO DRESS 2 COR ENERI TECHNO RE

For a population with 34 a score of X 31 corresponds to z 1 00 The standard deviation for the population is d 4 True False

6 8 and standard deviation 1 6 is a good description of the lowa Test vocabulary scores of seventh grade students in Gary Indiana This is a continuous probability model for the score of a randomly chosen student Call the score of a randomly chosen student X What is Prob X 10 a very small b 0 02 c 2 5 d 95 ibution with mean Question 6 3 0303 points Saved

female male total 236 148 95 222 82 55 458 230 150 479 359 838 Choose at random one Spring 2011 Math 1530 student What is the probability that the student gave the answer yes to the survey question PERCENT ANSWER TWO DECIMAL PLACES

The blood cholesterol level of all men aged 20 to 34 years follows the Normal distribution with mean 188 milligrams per decilliter mg dL and standard deviation 41 mg dL A sample survey measures the blood cholesterol level of a SRS of 10 such men The sample mean is denoted by The sampling distribution of the sample mean is a 188 mg dL and s 12 965 b approximately Normal with mean x 188 mg dL and standard deviation o 4 1 mg dL c approximately Normal with mean u x 59 451 mg dL and standard deviation 12 965 d approximately Normal with mean 188 mg dL and standard deviation o 12 965 mg dL

Psychologists often measure how long it takes mice to find their way through a maze The times for one particular maze follow an approximately Normal distribution with mean 18 seconds and standard deviation 3 seconds A researcher thinks that a loud noise will cause mice to complete the maze faster but not change the standard deviation She uses a loud noise to stimulate each of 10 mice right before she measures how long it takes each of them to complete the maze The sample mean is 16 2 seconds The appropriate null and alternative hypotheses for this test are Ho 18 seconds Ha 18 seconds The sample result is a not statistically significant at any level b statistically significant at the 5 level but not at the 2 level c proves that the mean time after a loud noise has changed to 116 2 seconds

The Survey of Study Habits and Attitudes SSHA is a psychological test that measures the motivation attitudes and study habits of college students Scores range from 0 to 200 and follow approximately a normal distribution with mean 115 and standard deviation o 25 You suspect that incoming freshman have a mean which is different from 115 since they are often excited yet anxious about entering college To verify your suspicion you test the hypotheses Ho M 115 H M 115 You give the SSHA to 25 students who are incoming freshman and find their mean score is 116 2 Assume that the scores of all incoming freshmen are approximately normal with the same standard deviation as the scores of all college students The value of the z test statistic for the given sample is then

For a population with u 100 and o 20 what is the X value corresponding to z 0 25 X 85 X 95 X 105 X 115

When you roll two fair six sided dice there are 36 possible outcomes that are equally likely B Let X the number of dots that turn up when two fair six sided dice are rolled Create a sampling distribution outcomes and probabilities for this X

The following data represent the weights in grams of a simple random sample of 50 candies Draw a boxplot of these data Use the boxplot and quartiles to decide if the distribution is symmetric 0 89 0 82 0 81 0 85 0 86 0 89 0 90 0 84 0 84 0 91 0 89 0 88 0 93 0 80 0 87 0 85 0 82 0 85 0 86 0 89 0 87 0 86 0 89 0 84 0 82 0 91 0 88 0 80 0 86 0 84 0 81 0 86 0 86 0 84 0 83 0 87 0 84 0 79 0 83 0 82 0 89 0 92 0 86 0 85 0 88 0 77 0 91 0 82 0 82 0 85 Draw a boxplot of the data Choose the correct graph below O A Weight of Candies T 0 76 0 80 0 84 0 88 0 92 Weight in grams Q B Weight of Candies TTTTTTT 0 76 0 80 0 84 0 88 0 92 Weight in grams Q possible OC Weight of Candies 0 76 0 80 0 84 0 88 0 92 Weight in grams Q E

The most recent NHANES report gives data for an SRS of 654 women aged 20 to 29 years The mean BMI of these 654 women was 26 8 On the basis of this sample we want to estimate the mean BMI u in the population of all 18 million women in this age group Past research has shown that the standard deviation for this population is 7 5 Based on the one sample used in the report we have O a 95 proof that the next sample mean will be in the same interval b 95 confidence that the population mean BMI is in the answer interval c the fact that the population mean BMI is 26 8 95 of the time d 95 evidence that any random 20 to 29 year old woman must have BMI between 26 21 and 27 39

A professor standardizes exam scores so that all exams have 100 and d 15 If the original scores from the exam have 56 and d 5 then a student with an original exam score of X 50 would receive a standardized score of X 82 True False

Dishonest people try to fake numbers in tax returns invoices or expense account laims It s actually hard to make up numbers that are fully realistic One reason is that the first digits of numbers in legitimate records often follow a model known as Benford s Law Call the first digit of a randomly chosen record X for short Benford s Law gives this probability model for X First digit 1 2 3 4 5 6 7 8 9 X probability 0 301 0 176 0 125 0 097 0 079 0 067 0 058 0 051 0 046 For instance if ABC company has been keeping legitimate records of its accounts the probability that a randomly chosen record starts with the number 7 is 0 058 A company without this probability has been jiggering its records somehow Reference Benford s law If Tembo Safaris keeps legitimate records what percent of those records will start with the digits 5 6 or 7

During World War II 12 000 able bodied male undergraduates at the University of Illinois participated in required physical training Each student ran a timed mile Their individual times followed the Normal distribution with mean 7 11 minutes and standard deviation 0 74 minutes One SRS of n 100 of these students had mean time 7 15 minutes Another SRS of n 100 of these students had mean 6 97 minutes After many SRS s the many values of the sample mean would follow the Normal distribution with O a mean x 7 11 minutes but standard deviation cannot be determined from the information given b mean x 7 11 minutes and standard deviation 0 074 minutes O c 7 11 and s 0 074 d mean 7 11 minutes and standard deviation 0 74 minutes

Choose a person aged 19 to 25 years at random and ask In the past seven days how many days did you go to an exercise or fitness center or work out Call the response X for short Based on a large random sample survey here is a probability model for the answer you will get Days probability 0 1 2 3 0 68 0 05 0 08 4 5 6 0 05 0 04 0 01 7 0 02 What is the probability that X 2 THE PROBABILITIES ARE GIVEN IN DECIMAL FORM YOUR ANSWERS SHOULD ALSO BE IN DECIMAL FORM

2 Party Republican Democrat Female Male 115 103 179 105 150 150 Independent Is there an association between party affiliation and gender a Construct a frequency marginal distribution b Construct a relative frequency marginal distribution c What proportion of registered voters considers themselves to be Independent d Construct a conditional distribution of party affiliation by gender e Draw a bar graph of the conditional distribution found in part d f Is gender associated with party affiliation If so how

Complete parts a through h for the data below 40 70 80 D 63 46 33 X y 30 30 y 50 60 58 53 X 90 b Find the equation of the line containing the points 50 58 and 80 33 0 30 299 3 or simplified fractions 90 304 0 100

A survey asks questions about one s happiness and health One would think that health plays a role in one s happiness Use the data in the accompanying table to determine whether healthier people tend to also be happier Treat level of health as the explanatory variable Click the icon to view the data table Create a conditional distribution for the data Level of Happiness Not too happy Pretty happy Very happy Total M Data table Poor Not too happy happy Poor 694 950 Level of Health Fair Fair 1 366 3 817 1002 Good Good 1 629 9 642 4 520 Excellent Excellent 742 5 185 5 095 C X Clear all

One of the biggest factors in determining the value of a home is the square footage The accompanying data represent the square footage and selling price in thousands of dollars for a random sample of homes for sale in a certain region Complete parts a through h below Click the icon to view the housing data FEED c Determine the linear correlation coefficient between square footage and asking price r 0 913 Round to three decimal places as needed d Is there a linear relation between square footage and asking price Yes No e Find the least squares regression line treating square footage as the explanatory varia y x Round the slope to three decimal places as needed Round the intercept to one decimal Data Table Square Footage x 2189 3223 1155 2064 3237 2654 4270 2235 2550 1744 1844 3986 Selling Price 5000s 377 4 380 7 194 1 1 352 640 1 351 6 652 4 380 9 415 8 303 9 279 9 717 7

23 What is the score at the 40th percentile point

A survey of 1030 randomly selected registered United States voters was conducted in which survey participants were asked What is your political affiliation Results of the survey by gender are shown below Complete parts a and b below Political Affiliation Gender Female Male Democrat 270 146 Independent 182 109 a Complete the following statement In the contingency table shown the Republican 151 172 This is a reading assessment question Be certain of your answer because you only get one attempt on this question variable is gender and the variable is political affiliation

What is the coefficient of determination for Data Set B X 3 6 8 3 0 5 1 4 8 2 Data Set A y 5 9 4 3 8 3 0 3 6 8 8 9 15 0 4 8 6 0 14 9 11 9 9 8 15 0 4 7 13 0 Data Set B X 3 1 W765911 14 9 4 1 2 2000N 1 0 9 0 5 0 3 4 7 4 0 1 7 5 y 8 9 15 0 4 8 6 0 14 9 11 9 9 8 15 0 4 7 13 0 X 2 8 IN o 3 o 8 1 Full Data Set Data Set C 03 3 0 8 3 8 2 755 1 4 1 0 7 9 066 5 9 5 0 y 8 9 15 0 4 8 6 0 14 9 11 9 9 8 15 0 4 7 13 0 This is a reading assessment question Be certain of your answer because you only get one attempt on this question The coefficient of determination for Data Set B is Type an integer or decimal rounded to the nearest tenth as needed

e data set given in the accompanying table Complete parts a through d Click the icon to view the data table a Construct a frequency marginal distribution Y Y Marginal distribution X 20 30 X2 25 25 X3 30 50 Marginal distribution Data table Y Y2 4 X 20 30 X2 25 25 X3 30 50 C