Statistics Questions and Answers

QUESTION 47 Suppose you computed r 0 817 using n 13 data points Using the critical values table below determine if the value of r is significant or not df CV and df CV and df CV and df CV and 1 0 997 11 0 555 21 0 413 40 2 0 950 12 0 404 50 3 0 878 13 0 396 60 4 0 811 14 0 388 70 5 0 754 15 0 381 80 6 16 90 0 707 0 666 17 100 0 632 18 19 0 602 0 576 20 7891 10 Select the correct answer below 0 532 0 514 0 497 0 482 0 468 0 456 0 444 0 433 0 423 22 23 24 25 26 27 28 29 30 0 374 0 367 0 361 0 355 0 349 Or is significant because it is between the positive and negative critical values r is not significant because it is between the positive and negative critical values r is significant because it is not between the positive and negative critical values T is not significant because it is not between the positive and negative critical values 0 304 0 273 0 250 0 232 0 217 0 205 0 195

QUESTION 50 2 POINTS Researchers are conducting a pooled left tailed two mean hypothesis test at a 1 significance level The two samples have sizes n 19 and n 14 The next step for the researchers is to find the critical value s for the hypothesis test Determine the critical value s for this test df to 10 Select all correct answers Select all that apply 2 453 2 449 2 445 2 445 31 32 33 34 to 05 to 025 to 01 to 005 1 309 1 696 2 040 2 453 2 744 1 309 1 694 2 037 2 449 2 738 1 308 1 692 2 035 2 445 2 733 1 307 1 691 2 032 2 441 2 728

The answer choices below represent different hypothesis tests for annual return of mutual funds Which of the listed below is a left tailed test Select all correct answers Select all that apply H p 18 Ha p 18 Ho 19 3 H 19 3 H p 8 H 8 Ho 11 3 H p 11 3 Ho 23 7 Hap 3 7

The data show the hourly earnings in dollars of a sample of 25 railroad equipment manufacturers Use technology to answer parts a and b 15 65 18 75 14 55 15 75 14 35 13 95 17 50 17 55 13 80 14 25 19 05 15 40 15 25 19 50 16 00 16 50 16 35 15 30 15 05 19 15 15 25 16 30 17 70 18 35 15 25 a Find the data set s first second and third quartiles Q Q3 Type integers or decimals Do not round b Draw a box and whisker plot that represents the data set Choose the correct answer below Note that different technologies will produce slightly different results O A O B O C Q

This problem asks you to draw the histogram for the following GFDT of test scores Score 40 44 45 49 50 54 On the graph below draw a histogram for this data set 30 34 35 39 This is best accomplished by following this protocol start by clicking on the lower left corner of the left most bar draw each consecutive bar by clicking in order the upper left corner the upper right corner the lower right corner repeat last step until all bars are drawn 5 Frequency 8 1 0 5 7 Also we will want the bar to span the class width which is 5 Thus a bar meant to span the values 5 9 would actually span 4 5 to 9 5 all the values that might round to 5 thru 9 H 10 9 8 7 6 4 3 2

Compute the mean and standard deviation of the random variable with the given discrete probability distribution P x 6 0 17 2 0 07 2 0 24 4 0 28 6 0 24 Send data to Excel Part 1 of 2 a Find the mean Round the answer to three decimal places if necessary The mean is 1 6 Part 2 of 2 b Find the standard deviation Round the answer to three decimal places if necessary 50 20 ola B

Heights of the tallest buildings in LA through 2016 in feet 1099 1018 858 750 748 735 725 723 717 699 699 667 625 620 578 571 571 560 534 533 517 516 506 496 493 491 478 463 454 454 454 450 443 417 414 1 Make a Histogram with 10 classes a Frequency Table class width classes frequency b Histogram label axes show scales used 2 Make a Relative Frequency Polygon based on your Histogram in problem 1 a midpoints freq rel freq b Relative Frequency Polygon label axes show scales used c Distribution Shape 3 Make a Cumulative Frequency Graph ogive based on your Histogram in problem 1 Upper Class a Limits Frea Cum Freg b Cumulative Frequency Graph

CHECK YOUR UNDERSTANDING CYU In the dialog box provided work the following problem Submit your work by inserting an image or uploading a single PDF file Percent of 16 Year Old Drivers Year f 1998 1999 2000 2001 2002 2003 2004 Percent of 16 Year Olds with Driver s Licenses L 44 0 37 0 34 0 32 5 31 5 30 5 30 0 Source Federal Highway Administration Average Rate of Change Find the average rate of change for the three blank areas

Another measure of central tendency is the trimmed mean It is computed by determining the mean of a data set after deleting the smallest and largest observed values Compute the trimmed mean for the data given in the accompanying table whose mean is 0 874 Is the trimmed mean resistant Click the icon to view the data table The trimmed mean is Round to the nearest thousandth as ne Data Table 0 87 0 91 0 89 0 83 0 91 0 88 0 90 0 88 0 88 0 94 0 82 0 90 0 90 0 86 0 86 0 86 0 91 0 86 0 87 0 93 0 96 0 87 0 93 0 91 0 91 0 86 0 89 0 87 0 88 0 89 0 77 0 82 0 88 0 84 0 93 0 81 0 92 0 85 0 84 0 84 Ne 0 84 0 84 0 88 0 87 0 88 0 85 0 84 0 83 0 90 0 86

ne table below gives the number of elementary school children in 16 school stricts in a particular region a Construct a cumulative frequency distribution b Construct a cumulative relative frequency distribution c Draw a frequency polygon d Draw a relative frequency ogive Number of Elementary School Students in 16 School Districts 1245 2400 4458 2500 1260 2991 3110 4800 2294 1050 1931 2287 2885 4400 4697 3640 a Complete the cumulative frequency distribution Students in a District 1000 1999 2000 2999 3000 3999 4000 4999 Cumulative Frequency

Each of the following three data sets represents the IQ scores of a random sample of adults IQ scores are known to have a mean and median of 100 Full data set a 107 107 105 107 105 93 116 98 102 102 93 102 93 100 95 110 Sample of Size 5 114 92 Sample of Size 12 114 92 96 119 Sample of Size 30 114 96 110 108 109 92 119 112 111 109 96 96 108 96 108 118 106 115 116 104 116 104 95 111 96 MTV Ve p ww Save 109 6 Type an integer or decimal rounded to one decimal place as needed What is the mean of the new sample of size 30 107 6 Type an integer or decimal rounded to one decimal place as needed What is the median of the new sample of size 5 102 Type an integer or decimal rounded to one decimal place as needed What is the median of the new sample of size 12 104 5 Type an integer or decimal rounded to one decimal place as needed What is the median of the new sample of size 30 7 Type an integer or decimal rounded to one decimal place as needed

In a certain state pickup trucks account for 25 of the state s registered vehicles If 200 registered vehicles a selected at random what is the expected number of pickup trucks The expected number of pickup trucks is

Because the mean is very sensitive to extreme values it is not a resistant measure of center By deleting some low values and high values the trimmed mean is more resistant To find the 10 trimmed mean for a data set first arrange the data in order then delete the bottom 10 of the values and delete the top 10 of the values then calculate the mean of the remaining values Use the axial loads pounds of aluminum cans listed below for cans that are 0 0111 in thick Identify any outliers then compare the median mean 10 trimmed mean and 20 trimmed mean 246 261 268 274 277 280 281 282 284 284 287 288 289 292 294 295 296 300 312 507 Compare the values Choose the correct answer below OA The median untrimmed mean and 20 trimmed mean are close to each other However the 10 trimmed mean is significantly different from those values OB The median 10 trimmed mean and 20 trimmed mean are close to each other However the untrimmed mean is significantly different from those values OC The median untrimmed mean and 10 trimmed mean are close to each other However the 20 trimmed mean is significantly different from those values OD All of the values are close to each other OE The untrimmed mean 10 trimmed mean and 20 trimmed mean are close to each other However the median is significantly different from those values

When finding the 37th percentile from a sample of IQ scores the locator L is found to be 45 5 What is the value of the 37th percentile Choose the correct answer below OA The IQ score that is midway between the 45th and 46th scores in the sorted list OB The IQ score that is midway between the 37th and 38th scores in the sorted list C The 46th IQ score in the sorted list D The 45th IQ score in the sorted list

Refer to the table summarizing service times seconds of dinners at a fast food restaurant How many individuals are included in the summary Is it possible to identify the exact values of all of the original service times Time sec 60 119 120 179 180 239 240 299 300 359 individuals are included in the summary Type a whole number Is it possible to identify the exact values of all of the original service times Frequency 8 23 14 1 5 O A No The frequency distribution tells nothing about the data values that fall below the lowest class limit or ab the highest class limit OB Yes The data values in each class are spread evenly across the full length of the class OC No The data values in each class could take on any value between the class limits inclusive OD Yes The data values in each class are equal to the corresponding class midpoint

A survey of adult men and women asked Which one of the following jobs would you most like to have The results of the survey are shown in the table a Construct a relative frequency distribution for men and women b Construct a side by side relative frequency bar graph c What are the apparent differences in gender as it pertains to this question a Complete the table below Job A B C D Men Women Not sure Round to three decimal places as needed Job A B C D Not sure Men 40 26 12 14 7 Women 16 39 12 14 19

The data in the accompanying table represent the land area and highest elevation for each of seven states of a country Complete parts a and b Click the icon to view the data table a Would it make sense to draw a pie chart for land area O Yes No

A national survey asked people How often do you eat out for dinner instead of at home The frequencies were as follows Complete parts a through g Response Never Rarely Sometimes Most of the time Always Frequency 239 457 942 325 61 a Construct a relative frequency distribution of data Response Relative Frequency Never Rarely Sometimes Most of the time Always Round to three decimal places as needed

What is a bar graph What is a Pareto chart What is a bar graph A A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories The height of each rectangle represents the category s frequency or relative frequency OB A bar graph is a circular graph that uses bars to divide it into segments corresponding to each category The segments are proportional to the frequency of its category OC A bar graph represents the frequencies of values either from left to right or right to left The different segmen of the bar are used to indicate the different frequencies of each category What is a Pareto chart OA A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency OB A Pareto chart is a combination of a pie chart and a bar graph OC A Pareto chart is a display of two data sets side by side where the height of each rectangle represents the category s frequency or relative frequency

frequency distribution lists the istribution lists the of occurrences of each category of data while a relative frequency of occurrences of each category of data

Review the following histogram How many data points were in the interval 35 2 46 8 1 3 6 Frequency 30 25 20 15 10 5 0 12 23 6 Leadership Scores 6 3 16 23 6 35 2 35 2 46 8 46 8 58 4 24 58 4 70

You are collecting data about your classmates favorite colors Which chart might be most helpful for representing the data A Scatter plot B None of these C Box and whisker D Histogram

Why might you use a pareto chart to represent data A If you want to visualize how often data falls in certain intervals B If you want to show the averages and outliers C If you want to see cumulative percentages of data in various intervals D If you want to show how data changes over time

In a box and whisker chart what information do you learn from the position of the whiskers A The inter quartile range B The maximum and minimum of the data values The outliers of the data set D The median

dz dz Draw a dependency diagram and write a chain rule formula for and dq dr z f x y x m q r y g q r Choose the correct dependency diagram for dz dq O A X dx dq Z 9 dz dy dy q OB X dq dx Z 318 V z 15 O C aq dz 9 2 918 dq 66 given the functions below O D dz dy 8 Z dz dx y dq

The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 6 days Suppose that one individual is randomly chosen Let X time to pass the kidney stone a What is the distribution of X X N b Find the probability that a randomly selected person with a kidney stone will take longer than 11 days to pass it Round to 4 decimal places

The Acme Company manufactures widgets The distribution of widget weights is bell shaped The widget weights have a mean of 40 ounces and a standard deviation of 10 ounces Use the Standard Deviation Rule also known as the Empirical Rule see image below Do not use normalcdf on your calculator Suggestion sketch the distribution in order to answer these questions a 68 of the widget weights lie between b What percentage of the widget weights lie between 10 and 50 ounces c What percentage of the widget weights lie above 20 0 15 2 35 13 5 34 34 and 13 5 2 35 015 de

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 5 days Let X be the number of days for a randomly selected trial Round all answers to 4 decimal places where possible a What is the distribution of X X N b If one of the trials is randomly chosen find the probability that it lasted at least 19 days c If one of the trials is randomly chosen find the probability that it lasted between 21 and 26 days

The scores on a standardized test are normally distributed with a mean of 100 and standard deviation of 10 What test score is 2 5 standard deviations above the mean

An engineer wants to determine how the weight of a gas powered car x affects gas mileage y The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year Complete parts a through d below Weight pounds x 3721 3837 2652 3630 3296 2990 3664 2642 3392 3836 Miles per Gallon y 18 16 25 19 22 23 16 25 20 17 b Interpret the slope and y intercept if appropriate Choose the correct answer below and fill in any answer boxes in your choice Use the answer from part a to find this answer OA For every pound added to the weight of the car gas mileage in the city will decrease by mile s per gallon on average It is not appropriate to interpret the y intercept miles per gallon on average It is not appropriate to interpret OB A weightless car will get the slope OC For every pound added to the weight of the car gas mileage in the city will decrease by mile s per gallon on average A weightless car will get miles per gallon on average D It is not appropriate to interpret the slope or the y intercept

Find the critical value s and rejection region s for the type of z test with level of significance x Include a graph with your answer Right tailed test 0 03 The critical value s is are z Round to two decimal places as needed Use a comma to separate answers as needed Select the correct choice below and if necessary fill in the answer box to complete your choice Round to two decimal places as needed OA The rejection regions are z and z B The rejection region is z C The rejection region is z Choose the correct graph of the rejection region below O A Z 0 Z Q O B 0 Z O C Z 0 Z O D A 0 Z

6 Given the shaded area to the left of 1 8 is 0 195 and the area to the left of 0 8 is 7100 answer the following questions a Find the area under the curve to the right of 1 8 b Find the area of the curve to the left of 0 c Find the area of the shaded region between 1 8 and 0 8 3 0 1 2

The technique works for equations of any order for example first order If is a solution of the differential equation y 5x 4 y 0 then its coefficients a satisfy the following recurrence relation For k 0 ak 2 0 We also have y 1 a1 0 ao help numbers Therefore write the first few terms of a solution where y 0 1 9 2 81 40 x ak 1 0 y akak k 0 2 916 8 help numbers x x ak help formulas

Determine the moment about point P if F 100 N and the angle alpha is 60 degrees P 2 m 1 m F

The table below shows the respective probabilities that a number of power failures will strike a certain subdivision in any given year with mean E X 1 9 and variance mean and the variance of the random variable Z 3X 8 probability power failures 0 2 0 0 1 1 0 3 2 E Z Type an integer or a decimal Do not round o2 Type an integer or a decimal Do not round 0 4 3 ox 1 29 Find

1 For the random variable with the given discrete probability distribution find the following Show your work to get credit 10 pt each Mean P x c P 2 b Standard deviation 0 0 45 d P 0 or 3 P less than or equal 2 1 0 05 2 0 10 3 0 25 4 0 15

a Place the digits 7 9 10 11 and 12 in the circles to make the sums across and vertically equal 28 b Is there more than one answer to part a a Choose the correct answer below OA 10 10 11 OC 10 OD 9 10

Scientists testing a new type of random number generator produced this set of data 51 49 18 51 50 31 52 49 51 34 Find the mean and standard deviation of this data Ox 43 60 and s 11 74 O 43 60 and o 11 74 X 51 and s 43 60 X 43 60 and s 49 5

ba Operfectly symmetric roughly symmetric C The overall shape of this graph is definitely skewed left 1 10 definitely skewed right 20 30 Acceptance Rate 40

Assume a population of 42 49 52 and 58 Assume that samples of size n 2 are randomly selected with replacement from the population Listed below are the sixteen different samples Complete parts a through c 42 42 42 49 52 49 52 42 42 52 52 52 42 58 52 58 49 42 58 42 49 52 58 52 a Find the median of each of the sixteen samples then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values Use ascending order of the sample medians Sample Median Probability Sample Median Probability V A V V Type integers or simplified fractions Use ascending order of the sample medians b Compare the population median to the mean of the sample medians Choose the correct answer below 49 49 58 49 OA The population median is equal to the mean of the sample medians OB The population median is not equal to the mean of the sample medians it is also not half or double the mean of the sample medians OC The population median is equal to half of the mean of the sample medians O D The population median is equal to double the mean of the sample medians c Do the sample medians target the value of the population median In general do sample medians make unbiased estimators of population medians Why or why not The complo medians do not forget the population median so sample medians are unbiased estimators because the mean of the sample medians does not 49 58 58 58 2

Suppose you computed r 0 817 using n 13 data points Using the critical values table below determine if the value of r is significant or not df CV and df 1 0 997 11 2 0 950 3 0 878 4 0 811 5 0 754 6 0 707 0 666 0 632 0 602 0 576 7 8 9 10 12 13 14 15 16 17 18 19 20 CV and 0 555 Select the correct answer below 0 532 0 514 0 497 0 482 0 468 0 456 0 444 0 433 0 423 r is significant because it is between the positive and negative critical values r is not significant because it is between the positive and negative critical values r is significant because it is not between the positive and negative critical values r is not significant because it is not between the positive and negative critical values df CV and 21 0 413 0 404 0 396 0 388 0 381 0 374 0 367 0 361 0 355 0 349 22 23 24 25 26 27 28 29 30 df 40 50 60 70 80 90 100 CV an 0 304 0 273 0 250 0 232 0 217 0 205 0 195

Assume that we want to construct a confidence interval Do one of the following as appropriate a find the critical value t 2 b find the critical value Za 2 or c state that neither the normal distribution nor the t distribution applies The confidence level is 90 o is not known and the histogram of 58 player salaries in thousands of dollars of football players on a team is as shown 4 Select the correct choice below and if necessary fill in the answer box to complete your choice O A ta 2 Round to two decimal places as needed OB Z 2 Round to two decimal places as needed OC Neither the normal distribution nor the t distribution applies 5 possible Frequency 40 30 20 10 0 4000 8000 12000 16000 20000 Salary thousands of dollars

Use technology and a t test to test the claim about the population mean at the given level of significance using the given sample statistics Assume the population is normally distributed Claim 75 x 0 10 Sample statistics x 77 6 s 3 5 n 29 OC Ho 75 HA 75 What is the value of the standardized test statistic The standardized test statistic is Round to two decimal places as needed What is the P value of the test statistic P value Round to three decimal places as needed Decide whether to reject or fail to reject the null hypothesis Choose the correct answer below A Reject Ho There is enough evidence to support the claim B Fail to reject Ho There is not enough evidence to support the claim C Reject Ho There is not enough evidence to support the claim D Fail to reject Ho There is enough evidence to support the claim O D Ho 75 HA H 75

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a p v 4 7v 2 lim p v lim 4 7v 2 v 1 4 4 lim 7v 2 v 1 4 Find p 1 p 1 4V 4 lim 7 2 v 1 lim v 1 7 lim v 1 4 7 1 2 7v lim 2 v 1 v a 1 lim 2 v 1 by the Sum Law by the Product Law by the Sum Law IN by the Sum Law by the Constant Multiple Law Thus by the definition of continuity p is continuous at a 1

George is studying the relationship between the number of employees at various companies and the amount of monthly overtime offered to employees and has collected the data shown in the table The line of best fit for the data is y 0 79z 98 8 Number of Employees Monthly Overtime in hours 30 75 40 68 58 52 50 60 a According to the line of best fit what would be the predicted number of monthly overtime hours for 27 employees at a company Sorry that s incorrect Try again The predicted number of monthly overtime hours is 77

Don t drink and drive A highway safety council reported that there were 3942 fatalities among drivers in auto accidents in particular year Following is a frequency distribution of their ages Approximate the mean age Round your answer to one deci place Age 11 20 21 30 31 40 41 50 51 60 61 70 Number of Fatalities 319 1544 827 693 429 130 Send data to Excel The mean is approximately

The scatter plot below shows data relating total income and the number of children a family has Which of the following patterns does the scatter plot show Income thousands 200 150 100 50 me e 000 5 1 2 3 Number of children Select the correct answer below O Positive linear pattern Positive linear pattern with deviations O Negative linear pattern O Negative linear pattern with deviations

Bill has an orange that weighs 6 ounces and an apple that weighs 7 ounces ie 199 grams Which fruit is relatively heavier and why Paragraph B V v

NUMATOMEM VAG PRAVY In a study conducted by the mechanical engineering department at a university the steel rods supplied by two different companies were compared Ten sample springs were made out of the steel rods supplied by each company and a measure of flexibility was recorded for each The data are provided in the accompanying table Compute both the mean and the variance in flexibility for both company A and company B Does there appear to be a difference in flexibility between company A and company B Click the icon to view the flexibility data The mean for company A is 8 Type integers or decimals Do not round The mean for company B is The variance for company A is The variance for company B is Round to four decimal places as needed Does there appear to be a difference in flexibility between company A and company B here CYTE to be a difference in flexibility Company A s sample mean is company B s variance company B s sample mean and company A s variance is Flexibility of Springs Company A 8 7 6 7 8 2 8 0 00 00 7 2 6 0 02 8 8 4 46 8 6 00 96 8 9 6 6 40 A n

Let X be a random variable with the probability distribution below Find Hg x where g x 2X 4 f x 3 3 Hg x 0 Simplify your answer 6 1 6 9