Statistics Questions

a x Special triangles Write answers in simplest radical form b 6 y y 60 V 30 21 8 5 V V y X 60 X 5 2 y

a x special triangles Write answers in simplest radical form b 2 3 X y 45 y UI 45 V 21 4 6 V c P X y 6 45 6

In right triangle ABC side a 43 and m A 65 Find the lengths of side band side c c is the hypotenuse Round answers to the nearest tenth b C

6 In right triangle ABC side c 22 and m A 40 Find the lengths of side a and side 6 Round answers to the nearest tenth A2 b

Solve for Leave answer in simplified radical form X x 45 5

A right triangle ABC is shown Find the measure of angle C Round answer to the nearest tenth 4 17 15 A 8 B m C degrees

Find the values of x and y Round answers to the nearest tent 12 cm 80

31 Exercise and type 2 diabetes It is generally accepted that regular exercise provides health benefits to indi viduals with type 2 diabetes although the exact exercise regimen aerobic vs resistance vs both is unclear The subjects in this study were sedentary 30 to 75 year old adults with type 2 diabetes and elevated hemoglobin Alc levels above 6 5 The level of hemoglobin Alc correlates very well with a person s recent overall blood sugar levels If the blood sugars have generally been run ning high during the previous few months the level of hemoglobin Alc will be high In a randomized con trolled study 41 subjects were assigned to a nonexer cise control group 73 to resistance training only 72 to aerobic exercise only and 76 to combined aerobic and resistance training The weekly duration of exercise was similar for all three exercise groups and subjects remained on the exercise regimens for nine months At the end of nine months the hemoglobin A1c levels of

1 Road Rage The phenomenon of road rage has been frequently discussed but in frequently examined So begins a report based on interviews with 1382 randomly selected drivers The respondents answers to interview questions produced scores on an angry threatening driving scale with values between 0 and 19 What driver characteristics go with road rage There were no significant differences among races or levels of education What about the effect of the driver s age Here are the mean responses for three age groups 30 yr 2 22 30 55 yr 1 33 55 yr 0 66 The report says that F 34 96 with P 0 01 hat are the null and alternative hypotheses for the ANOVA F test Be sure to explain what means the test compares b Based on the sample means and the F test what do you conclude

For each problem select the best response a A researcher wishes to determine whether the rate of water flow in liters per second over an experimental soil bed can be used to predict the amount of soil washed away in kilograms In this study the explanatory variable is the A size of the soil bed OB rate of water flow OC amount of eroded soil OD depth of the soil bed O E None of the above b The Columbus Zoo conducts a study o determine whether a household s income can be used to predict the amount of money the household will give to the zoo s annual fund drive The response variable in this study is OA a household s income OB all households in Columbus C the Columbus Zoo O D the amount of money a household gives to the zoo s annual fund drive OE None of the above c A researcher measures the correlation between two variables This correlation tells us OA whether a cause and effect relation exists between two variables OB whether or not a scatterplot shows an interesting pattern OC the strength of a straight line relation between two variables OD whether there is a relation between two variables E None of the above

11 What Music Will You Play People often match their behavior to their social environment One study of this idea first established that the type of music most preferred by black college students is R B and that whites most preferred music is rock Will students hosting a small group of other students choose music that matches the makeup of the people attending Assign 90 black business students at random to three equal sized groups Do the same for 96 white students Each student sees a picture of the people he or she will host Group 1 sees six blacks Group 2 sees three whites and three blacks and Group 3 sees six whites Ask how likely the host is to play the type of music preferred by the other race Use ANOVA to compare the three groups to see whether the racial mix of the gathering affects the choice of music a For the white subjects F 16 48 What are the degrees of freedom b For the black subjects F 2 47 What are the degrees of freedom

29 Perceived exertion while exercising Can the introduc tion of pleasant sensory stimuli lead to a more pleasant exercise environment and decrease perceived exertion during a four minute stepping task Forty three stu dents from a Southeastern university were assigned at random to three conditions taste in which partici pants inserted a lemon flavored mouth guard during the task placebo in which participants inserted a non flavored mouth guard and control in which no mouth guard was used Twelve students were assigned to the taste group 15 to the placebo group and 16 to the control group Ratings of perceived exertion RPE scores were measured on standard 15 point scale rang ing from 6 lue van liche to 20 Corrhoud 13

Fifty four wild bears were anesthetized and then their weights and chest sizes were measured and listed in a data set Results are shown in the accompanying display Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes When measuring an anesthetized bear is it easier to measure chest size than weight If so does it appear that a measured chest size can be used to predict the weight Use a significance level of 0 05 Identify the critical value s Round to three decimal places as needed A There are two critical values at r 0 268 OB There is one critical value at r falls between the critical values Correlation Results Correlation coeff r 0 950958 Critical r 0 2680855 P value two tailed 0 000 Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes Choose the correct answer below and if necessary fill in the answer box within your choice Round to three decimal places as needed A Yes because the absolute value of the test statistic 0 951 exceeds the critical value exceeds the critical value B No because the absolute value of the test statistic OC No because the test statistic OD Yes because the test statistic falls between the critical values OE The answer cannot be determined from the given information When measuring an anesthetized bear is it easier to measure chest size than weight If so does it appear that a measured chest size can be used to predict the weight OA Yes it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale The chest size could not be used to predict weight because there is not a linear correlation between the two OB No it is easier to measure weight than chest size because the chest is not a flat surface OC Yes it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale The chest size could be used to predict weight because there is a linear correlation between the two bort size than a weight because measuring weight would require lifting the bear onto the scale The chest size could not be used to predict weight because there is

10 Refer to the accompanying scatterplot a Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y b Find the value of the correlation coefficient r and determine whether there is a linear correlation c Remove the point with coordinates 1 9 and find the correlation coefficient r and determine whether there is a linear correlation d What do you conclude about the possible effect from a single pair of values Click here to view a table of critical values for the correlation coefficient a Do the data points appear to have a strong linear correlation Yes No b What is the value of the correlation coefficient for all 10 data points r 0 893 Simplify your answer Round to three decimal places as needed Is there a linear correlation between x and y Use a 0 01 A Yes because the correlation coefficient is not in the critical region B No because the correlation coefficient is not in the critical region C Yes because the correlation coefficient is in the critical region OD No because the correlation coefficient is in the critical region 0 O 10

Match these values of r with the accompanying scatterplots 0 998 0 404 1 0 757 and Click the icon to view the scatterplots Match the values of r to the scatterplots Scatterplot 1 r Scatterplot 2 r Scatterplot 3 r Scatterplot 4 r Scatterplot 5 r Scatterplots 0 2 4 A 6 8 0 15 T 14 13 12 11 9 10 Scatterplot 1 2 0 2 0 4 0 6 0 8 X Scatterplot 4 0 0 2 0 4 0 6 0 8 X 1 Q 5 B Q Q 0 A 8 6 4 2 0 0 0 2 0 4 0 6 0 8 X 8 6 4 2 0 Scatterplot 2 0 Scatterplot 5 0 2 0 4 0 6 0 8 X Q Q Q Q 3 0T 14 2 3 4 0 Scatterplot 3 0 2 0 4 0 6 0 8 X 1 Q Q 5

Fifty four wild bears were anesthetized and then their weights and chest sizes were measured and listed in a data set Results are shown in the accompanying display Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes When measuring an anesthetized bear is it easier to measure chest size than weight If so does it Determine the null and alternative hypotheses Ho P H p 0 Type integers or decimals Do not round Identify the correlation coefficient r r Correlation Results Correlation coeff r 0 950958 Critical r 0 2680855 P value two tailed 0 000 0 Round to three decimal places as needed

Use the given data set to complete parts a through c below Use 0 05 13 8 74 9 8 78 X y Click here to view a table of critical values for the correlation coefficient A a Construct a scatterplot Choose the correct graph below Ay 10 8 10 9 15 6 4 2 0 0 4 1 8 8 13 X 8 12 16 OB Ay 10 8 6 4 2 0 0 4 8 12 16 o 11 9 26 14 8 11 OC Ay 10 8 6 N 4 2 0 0 4 6 6 14 X OA There is insufficient evidence to support the claim of a nonlinear correlation between the two variables B There is sufficient evidence to support the claim of a nonlinear correlation between the two variables OC There is insufficient evidence to support the claim of a linear correlation between the two variables 8 12 16 Q 4 3 11 12 9 13 OD Ay 10 8 6 4 2 0 0 4 b Find the linear correlation coefficient r then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables The linear correlation coefficient is r 0 817 Round to three decimal places as needed 8 12 16 7 7 26 Q 5 4 7 Using the linear correlation coefficient found in the previous step determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables Choose the correc answer below

43 Determine the following a The 95th percentile of the chi squared distribution with 10 d P x 14 611 or x2 37 652 where x is a chi squared rv with v 25

The accompanying table lists the ages of acting award winners matched by the years in which the awards were won Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables Should we expect that there would be a correlation Use a significance level of 0 05 Click the icon to view the ages of the award winners Construct a scatterplot Choose the correct graph below O A O C Best Actor years 70 20 LI 20 70 Best Actress years B Best Actor years 70 20 LU 4 20 70 Best Actress years The linear correlation coefficient is r Round to three decimal places as needed Best Actor years 70 20 20 C GRA H 70 Best Actress years Best Actor years D 70 20 20 70 Best Actress years 21 202

Use the given data to find the equation of the regression line Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line X 10 9 y 7 68 6 67 A Ay Create a scatterplot of the data Choose the correct graph below 25 20 15 10 10 13 6 12 73 12 73 7 37 7 67 8 49 6 3 5 0 12 10 0 5 10 15 2 B Ay 25 20 15 10 5 0 0 5 10 15 2 O C 25 250 20 Ay 15 10 5 0 0 5 10 15 2 4 12 5 23 8 21 6 OD 25 20 15 10 50 Ay 0 5 10 15 2

Fill in the blank Given a collection of paired sample data the y bo b x algebraically describes the relationship between the two variables x and y Given a collection of paired sample data the y bo b x algebraically describes the relationship between the two variables y an

Find the regression equation letting the first variable be the predictor x variable Using the listed actress actor ages in various years find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 44 years Is the result within 5 years of the actual Best Actor winner whose age was 46 years Best Actress 29 32 28 59 31 34 44 28 63 22 44 Best Actor 43 36 36 47 50 48 59 53 38 58 46 Find the equation of the regression line y xx Round the y intercept to one decimal place as needed Round the slope to three decimal places

Listed below are the overhead widths in cm of seals measured from photographs and the weights in kg of the seals Construct a scatterplot find the value of the linear correlation coefficient r and find the critical values of r using a 0 05 Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals Overhead Width 7 0 Weight 111 Click here to view a table of critical values for the correlation coefficient A Aweight kg Construct a scatterplot Choose the correct graph below OB 300 100 7 width cm 10 Q 7 7 173 Aweight kg 300 100 width cm 9 8 247 10 The linear correlation coefficient is r 0 936 Round to three decimal places as needed 9 3 199 0 C Aweight kg 300 8 7 197 100 7 width cm 10 O O 8 1 184 D Aweight kg 300 100 width cm The critical values are r Round to three decimal places as needed Use a comma to separate answers as needed 10 Q 20

When making predictions based on regression lines which of the following is not listed as a consideration Choose the correct answer below OA Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well OB Use the regression equation for predictions only if the linear correlation coefficient r indicates that there is a linear correlation between the two variables OC Use the regression line for predictions only if the data go far beyond the scope of the available sample data OD If the regression equation does not appear to be useful for making predictions the best predicted value of a variable is its

Fill in the blank Paired sample data may include one or more points that strongly affect the graph of the regression line Paired sample data may include one or more are points that strongly affect the graph of the regression line which are which

Fill in the blank is the For a pair of sample x and y values the difference between the observed sample value of y and the y value that is predicted by using the regression equation For a pair of sample x and y values the is the difference between the observed sample value of y and the y value that of ya is predicted by using the regression equation

Fill in the blank In a scatterplot a n other data points In a scatterplot a n other data points is a point lying far away from the is a point lying far away from the

a Using the pairs of values for all 10 points find the equation of the regression line b After removing the point with coordinates 2 4 use the pairs of values for the remaining 9 points and find the equation of the regression line c Compare the results from parts a and b 68642 10 X A a What is the equation of the regression line for all 10 points y x Round to three decimal places as needed 0 0 2 4 6 8 10

Use the given data set to complete parts a through c below Use 0 05 8 8 13 13 8 74 9 8 78 X y Click here to view a table of critical values for the correlation coefficient a Construct a scatterplot Choose the correct graph below A Ay 10 8 6 4 10 9 15 2 0 0 d 4 8 12 16 Q OB Ay 10 8 6 4 2 0 X 4 8 12 16 Q G 11 9 26 14 8 11 C Ay 10 8 6 4 2 0 0 4 000 6 6 14 OA There is insufficient evidence to support the claim of a nonlinear correlation between the two variables OB There is sufficient evidence to support the claim of a nonlinear correlation between the two variables OC There is insufficient evidence to support the claim of a linear correlation between the two variables OD There is sufficient evidence to support the claim of a linear correlation between the two variables 8 12 16 Q 5 4 3 11 OD Ay 10 8 6 12 9 13 4 2 0 0 4 b Find the linear correlation coefficient r then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables The linear correlation coefficient is r 0 817 Round to three decimal places as needed 8 12 16 7 7 26 Q 5 4 74 Using the linear correlation coefficient found in the previous step determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables Choose the correct answer below

Which of the following is not a requirement for regression analysis Choose the correct answer below OA Visual examination of the scatterplot shows that the points approximate a straight line pattern OB Outliers can have a strong effect on the regression equation so remove any outliers if they are known to be errors C The sample of paired x y data is a random sample of quantitative data OD The method for regression analysis line is not robust It is seriously affected by a small departure from a normal distribution

Which of the following is not equivalent to the other three Choose the correct answer below O Explanatory variable O Predictor variable O Dependent variable O Independent variable

Fill in the blank In working with two variables related by a regression equation in a variable is the amount that it changes the when the other variable changes by exactly one unit In working with two variables related by a regression equation the in a variable is the amount that it changes when the other variable changes by exactly one unit

What is the relationship between the linear correlation coefficient r and the slope b of a regression line Choose the correct answer below OA The value of r will always be larger than the value of b OB The value of r will always have the same sign as the value of b C The value of r will always be smaller than the value of b D The value of r will always have the opposite sign of the value of b

a What is a residual b In what sense is the regression line the straight line that best fits the points in a scatterplot a What is a residual OA A residual is a value of y y which is the difference between an observed value of y and a predicted value of y OB A residual is the amount that one variable changes when the other variable changes by exactly one unit OC A residual is a point that has a strong effect on the regression equation D A residual is a value that is determined exactly without any error

Refer to the accompanying scatterplot a Examine the pattern of 10 all 10 points and subjectively determine whether there appears to be a strong correlation between x and y b Find the value of the correlation coefficient r and determine whether there is a linear correlation c Remove the point with coordinates 1 9 and find the correlation coefficient r and determine whether there is a linear correlation d What do you conclude about the possible effect from a a Do the data points appear to have a strong linear correlation Yes No 0 0 X TTT 10 b What is the value of the correlation coefficient for all 10 data points r as needed Simplify your answer Round to three decimal places E

59 Let X X X be a random sample from a uniform distribution on the interval 0 0 so that 0 x 0 0 0 otherwise f x Then if Y max X it can be shown that the rv U Y O has density function fu u foto nu 0 usl otherwise 0 a Use f u to verify that Y P a 2 1 a 2 1 and use this to derive a 100 1 a CI for 8 b Verify that P a Y 0 1 1 a and derive a 100 1 x CI for 0 based on this probability statement c Which of the two intervals derived previously is shorter If my waiting time for a morning bus is uniformly distributed and observed waiting times are x 4 2 x 3 5 x3 1 7 x 1 2 and x 2 4 derive a 95 CI for 0 by using the shorter of the two intervals 1

20 TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streaming is gaining in popularity The Harris poll reported on November 13 2012 that 53 of 2343 American adults surveyed said they have watched digitally streamed TV programming on some type of device a Calculate and interpret a confidence interval at the 99 confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time b What sample size would be required for the width of a 99 CI to be at most 05 irrespective of the value of p

0 A random sample of n 15 heat pumps of a certain type yielded the following observations on lifetime in years 2 0 1 3 6 0 1 9 5 1 4 1 0 5 3 15 7 7 4 8 9 12 2 5 3 6 a Assume that the lifetime distribution is exponential and use an argument parallel to that of Example 7 5 to obtain a 95 CI for expected true average lifetime b How should the interval of part a be altered to achieve a confidence level of 99 c What is a 95 CI for the standard deviation of the lifetime distribution Hint What is the standard deviation of an exponential random variable

45 Wire electrical discharge machining WEDM is a pro cess used to manufacture conductive hard metal compo nents It uses a continuously moving wire that serves as an electrode Coating on the wire electrode allows for cooling of the wire electrode core and provides an improved cutting performance The article High Performance Wire Electrodes for Wire Electrical Discharge Machining A Review J of Engr Manuf 2012 1757 1773 gave the following sample observa tions on total coating layer thickness in um of eight wire electrodes used for WEDM 21 16 29 35 42 24 24 25 Calculate a 99 CI for the standard deviation of the coating layer thickness distribution Is this interval valid whatever the nature of the distribution Explain

13 The article Gas Cooking Kitchen Ventilation and Exposure to Combustion Products Indoor Air 2006 65 73 reported that for a sample of 50 kitchens with gas cooking appliances monitored during a one week period the sample mean CO level ppm was 654 16 and the sample standard deviation was 164 43 a Calculate and interpret a 95 two sided confidence interval for true average CO level in the population of all homes from which the sample was selected b Suppose the investigators had made a rough guess of 175 for the value of s before collecting data What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95

1 Consider a normal population distribution with the value of o known a What is the confidence level for the interval x 2 810 n b What is the confidence level for the interval x 1 440 Vn c What value of Zal2 in the CI formula 7 5 results in a confidence level of 99 7 d Answer the question posed in part c for a confi dence level of 75

5 On the basis of extensive tests the yield point of a particular type of mild steel reinforcing bar is known to be normally distributed with o 100 The composition of bars has been slightly modified but the modification is not believed to have affected either the normality or the value of o a Assuming this to be the case if a sample of 25 modified bars resulted in a sample average yield point of 8439 lb compute a 90 CI for the true aver age yield point of the modified bar b How would you modify the interval in part a to obtain a confidence level of 92 EEN SERE TREN 20 p POLIMER W jehuize F P BEHER WERDEN

A psychologist counsels people who are getting divorced A random sample of ten of her patients provided the data in the following scatterplot where x number of years of courtship before marriage and y number of years of marriage before divorce What does the scatterplot reveal about the relationship between length of courtship and length of marriage Length of marriage years 20 0 No correlation 17 5 15 0 12 5 10 0 7 5 5 0 Weak positive correlation Moderate positive correlation Moderately weak correlation Marriage length vs courtship length Length of courtship years

A researcher wants to test if college students ages 18 25 consume more alcohol per year than non college students ages 18 25 They randomly selected 500 college students and found a mean of 89 6 liters of alcohol consumed with a standard deviation of 21 liters In comparison 450 randomly selected non college students had a mean of 87 1 liters of alcohol consumed with a standard deviation of 19 liters What would be the null and alternative hypotheses for this situation Ho Pc PN HA PC PN Ho MC N HAPC N Ho Mc N AC N Ho Pc UN HANC N Ho Pc PN HA PC PN

A researcher wants to test if college students ages 18 25 consume more alcohol per year than non college students ages 18 25 They randomly selected 500 college students and found a mean of 89 6 liters of alcohol consumed with a standard deviation of 21 liters In comparison 450 randomly selected non college students had a mean of 87 1 liters of alcohol consumed with a standard deviation of 19 liters What would be the null and alternative hypotheses for this situation Ho Pc PN HA PC PN Ho Pc N MATU PAN Ho Pc PN HA PCPN Ho Pc UN HA PC PN Ho Pc PN HA PC PN

Previous Problem Entered MUNOT 7 MU 77 10 2036 YES Problem List Next Problem Answer Preview MUNOT 7 MU 77 10 2036 At least one of the answers above is NOT correct YES Result incorrect correct correct correct Lois thinks that people living in a rural environment have a healthier lifestyle than other people She believes the average lifespan in the USA is 77 years A random sample of 10 obituaries from newspapers from rural towns in Idaho give 81 84 and s 1 5 Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years a State the null and alternative hypotheses Type mu for the symbol e g mu 1 for the mean is greater than 1 mu 1 for the mean is less than 1 mu not 1 for the mean is not equal to 1 Ho Ha Mu 77 b Find the test statistic t 10 20362 c Answer the question Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years Use a 10 level of significance Type Yes or No Yes

Engineers must consider the breadths of male heads when designing helmets The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6 3 inches and a standard deviation of 0 8 inches In what range would we expect to find the middle 39 of most head breadths Round the answer to two decimal places Between 6 10 and 6 50 Between If we were to draw samples of size 55 from this population in what range would you expect to find the middle 39 of most averages for the breadths of male heads in the sample Round the answer to two decimal places inches and inches

You really struggle remembering to bring your lunch to work Each day seems to be independent as to whether you remember to bring your lunch or not The chance that you forget your lunch each day is 39 1 Consider the next 46 days Let X be the number of days that you forget your lunch out of the 46 days Calculate the following Hx 17 98 ox 10 95 P X 18 11 98 P X 23 P X 14 P 16 X 19

Suppose the mean starting salary for nurses is 66 239 nationally The standard deviation is approximately 10 660 The starting salary is not normally distributed but it is mound shaped A sample of 40 starting salaries for nurses is taken State the random variable O The standard deviation of starting salaries of nurses O The mean starting salary of a nurse Starting salary for a nurse What is the mean of the sample mean H 66 239 What is the standard deviation of the sample mean Round to two decimal places 0 1685 49 What is the shape of the sampling distribution of the sample mean Why O You can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30 O You can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30 O You can t say anything about the sampling distribution of the sample mean since the population of the random variable is not normally distributed and the sample size is greater than 30 Find the probability that the sample mean is more than 72 000 Round to four decimal places P X 72000 Find the probability that the sample mean is less than 59 000 Round to four decimal places

You have a really annoying stapler that seems to randomly jam On any given attempt to staple it seems to independently jam 17 2 of the time a Out of 280 papers stapled what is the probability that your stapler will jam 41 times or fewer 0 145 b Find the mean and standard deviation for the number of jammed staples out of 280 attempts Mean 48 16 Standard Deviation 6 314 c Does the normal approximation apply Explain d Use the normal distribution without continuity correction 0 5 to find the probability that your stapler will jam 41 times or fewer out of 280 attempts e Use the normal distribution with continuity correction 0 5 to find the probability that your stapler will iam 41 times or fewer out of 280 attempts