Statistics Questions

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

Assume that a coin is tossed twice The coin may not be fair The sample space consists of the outcomes HH HT TH TT Is the given a probability model Choose one No Outcome HH Probability 0 16 HT TH TT 0 60 0 90 0 47

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

QUESTION 3 1 POINT Annie a pharmacist claims that a generic anti histamine dose is more than 18 mg on average Several of her coworker do not believe her so she decides to do a hypothesis test at a 10 significance level to persuade them She measures 18 pills collects the proper data and works through the testing procedure Ho 18 Ha 18 19 1 0 1 6 a 0 1 significance level The test statistic is 20 Select the correct answer below I Ho 19 1 18 1 6 18 2 92 The critical value is 20 1 1 28 Conclude whether to reject or not reject Ho and interpret the results O Reject Ho At the 10 significance level the test results are not statistically significant and at best provide weak evidence against the null hypothesis O Reject Ho At the 10 significance level the data provide sufficient evidence to conclude that the mean dosage is more than 18 mg O Do not reject Ho At the 10 significance level the test results are not statistically significant and at best provide weak evidence against the null hypothesis Do not reject Ha At the 10 significance level the data provide sufficient evidence to conclude that the mean dosage is more than 18 mg C

2 Compute and interpret the sample correlation for the following dataset x Y 4 50 11 40 3 60 16 30

Question Christine is the dean of students at a college She is concerned about the average amount of sleep students in the pre med program are getting Christine makes an inquiry on whether students who are enrolled in the pre med program are getting less sleep on average compared to pre law students The average number of hours of sleep per night for a random sample of 30 pre med students and 30 pre law students is recorded Assume that the population variances of hours of sleep per night for pre med students and for pre law students are not equal and that the hours of sleep per night for both groups of students are normally distributed Let the average number of hours of sleep per night for pre med students be the first sample and let the average number of hours of sleep per night for pre law students be the second sample She conducts a two mean hypothesis test at the 0 05 level of significance to test if there is evidence that pre med students are getting less sleep than pre law students a Which answer choice shows the correct null and alternative hypotheses for this test Select the correct answer below Ho M1 M2 Ha 1 2 which is a two tailed test Ho M1 M2 Ha M1 M2 which is a left tailed test Ho M1 M Ha M1 M2 which is a two tailed test Ho M M2 Ha M1 M2 which is a right tailed test

Which of the data sets represented by the following histograms has the smallest standard deviation Select the correct answer below O 40 30 20 10

z X X S when x 83 x 91 and z 2 3

Find the area to the right of the z score 1 40 and to the left of the z score 1 58 under the standard normal curve Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 1 3 0 9032 0 9049 0 9066 0 9082 0 9099 0 9115 0 9131 0 9147 0 9162 0 9177 1 4 0 9192 0 9207 0 9222 0 9236 0 9251 0 9265 0 9279 0 9292 0 9306 0 9319 1 5 0 9332 0 9345 0 9357 0 9370 0 9382 0 9394 0 9406 0 9418 0 9429 0 9441 1 6 0 9452 0 9463 0 9474 0 9484 0 9495 0 9505 0 9515 0 9525 0 9535 0 9545 1 7 0 9554 0 9564 0 9573 0 9582 0 9591 0 9599 0 9608 0 9616 0 9625 0 9633 1 8 0 9641 0 9649 0 9656 0 9664 0 9671 0 9678 0 9686 0 9693 0 9699 0 9706 1 9 0 9713 0 9719 0 9726 0 9732 0 9738 0 9744 0 9750 0 9756 0 9761 0 9767 Use the value s from the table above Provide your answer below

1 Complete the following tables A Height Percent Cumulative Inches Freq Freq Freq 64 69 70 75 76 81 82 87 88 93 5 2 6 4 3 C Relative B The data shows the sample of wages per hour Freq Compute the Z scores given mean is 30 and SD is 1 xi 50 40 70 30

How many kids In a survey 46 200 women were asked how many children they had The results were as follows Number of Number of Children Women 0 1 2 3 4 5 6 7 8 or more Part 1 of 4 Total Send data to Excel 12 598 7467 11 269 7038 3782 1820 925 522 779 46 200 a What is the probability that a sampled woman has three children Round your answer to four decimals The probability that a sampled woman has three children is 0 1523

stion A two mean nonpooled hypothesis test has two samples of sizes 1 11 and 1 19 The samples have standard deviations of s 4 and s 8 The degrees of freedom is found from the following calculation Select all correct answers Select all that apply 1 315 1 314 Determine the critical value s for a two mean hypothesis test at the 10 significance level if the hypothesis test is right tailed Ha 1 12 1 313 df 1 313 8 11 19 2 2 2 2 191 19 27 63 df to 10 to 05 to 025 to 01 to 005 26 1 315 1 706 2 056 2 479 2 779 27 1 314 1 703 2 052 2 473 2 771 28 1 313 1 701 2 048 2 467 2 763 29 1 311 1 699 2 045 2 462 2 756

The graphs below represent the performance evaluations of 3 managers labeled A B and C on the same axis Determine which normal distribution has the largest mean Select the correct answer below O A OB A

Researchers are conducting a nonpooled two tailed two mean hypothesis test at a 5 significance level The two samples have sizes n 13 and 1 25 The samples have standard deviations of 7 and s 6 The researchers computed the degrees of freedom to be 21 36 What is are the critical value s for this test Select all that apply 2 08 2 07 1 72 1 72 2 07 df 19 20 21 22 to 10 to os 1 328 1 729 1 325 1 725 to 025 to 01 Round your answer s to two decimal places Select all correct answers 2 093 1 321 1 717 2 074 2 539 to 005 2 086 2 528 2 845 2 861 1 323 1 721 2 080 2 518 2 831 2 508 2 819

Government 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 2004 and 2006 Use a TI 84 calculator to answer the following Organization Smithsonian Institution Corporation for Public Broadcasting Institute of Museum and Library Services National Gallery of Art Kennedy Center for the Performing Arts Source National Endowment for the Arts Send data to Excel Part 1 of 3 2004 489 377 262 88 17 2006 517 460 247 95 18

Age Range Less than 1 year 1 17 18 44 45 64 65 84 85 and up Total Send data to Excel art 1 of 3 What is the probability that an asthma patient is between 45 and 64 years old he probability that an asthma patient is between 45 and 64 years old is 0 2971 art 1 3 Number 7865 103 038 79 655 121 726 80 656 16 755 409 695 art 2 of 3 What is the probability than an asthma patient is less than 1 year old

Presidents and first ladies The following table presents the ages of 9 U S presidents and their wives on the first day of their presidencies Use a calculator to compute the following Name Barack and Michelle Obama George W and Laura Bush Bill and Hillary Clinton Ronald and Nancy Reagan Gerald and Betty Ford Lyndon and Lady Bird Johnson John and Jacqueline Kennedy Dwight and Mamie Eisenhower Harry and Bess Truman Send data to Excel Her Age 45 54 45 55 59 56 50 31 60 His Age 47 54 46 64 69 61 55 43 60

Which of the following is the best measure of the center of this data set 012 2 3 4 MathBits com Numbers of Brothers and Sisters range O median only mean or median mean only

Some researchers are doing a two mean pooled t test They have two samples with sizes n 25 and n 13 The population standard deviations are unknown but assumed to be equal so the sample standard deviations are found and used to calculate a pooled standard deviation sp For sample 1 s1 13 2 and 28 For sample 2 s2 14 2 and 2 37 What are the test statistic t and the degrees of freedom to perform this test Select the correct answer below if Sp 13 542 then t df 36 If s 13 542 then t df 36 If sp 13 542 then t df 38 If sp 13 542 then t df 36 25 13 13 542 25 13 13 542 28 37 13 542 V 28 1 28 37 28 37 13 542 2 59 3 54 2 65 1 94

Below is bivariate data on vintage dresser auctions where X is the year of construction of the dresser and Y is the price sold at auction X Y 1842 4500 b 1790 8600 1886 2100 1903 1900 454020 0 1819 7500 1880 1600 Answer the following questions and show your calculations or calculator keypresses to get full credit a 1851 4900 Find the correlation coefficient round to four decimal places between year of construction and price sold at auction Interpret the direction and strength of the correlation 30pt 7 56979700 12971 31100 VC7 24044831 12971 2 7 185050000 31100 4540200 4688017 133 0 96 66976 328140000 Find the Least Squares Regression Line Round to four decimal places throughout 20pt

ccording to a scientific journal an important property of a fiber is its water absorbency A random sample of 20 pieces of cotton fiber was taken and the absorbency measured The accompanying table shows the absorbency values Complete parts a through d below Click the icon to view the absorbency values a Calculate the sample mean and median for the sample values The sample mean is Round to three decimal places as needed The sample median is Round to three decimal places as needed b Compute the 10 trimmed mean The 10 trimmed mean is Round to three decimal places as needed Cotton Fiber Water Absorberley 18 72 23 86 19 33 21 47 19 34 21 62 19 28 21 67 20 82 20 38 18 91 20 58 22 17 19 73 18 03 Print 22 60 23 05 21 16 Done 20 20 O 22 81 X 1

How many individual scores are in the following distribution 432LO f 2 1 0 N 5 N 6 N 10 N 4 1 2 3 4 X

es a Calculate the centerline the upper control limit UCL and the lower control limit LCL for the chart if samples of size 9 are used Round the value for the centerline to the nearest whole number and the values for the UCL and LCL to 2 decimal places Centerline Upper Control Limit Lower Control Limit b Calculate the centerline the upper control limit UCL and the lower control limit LCL for the x chart if samples of size 18 are used Round the value for the centerline to the nearest whole number and the values for the UCL and LCL to 2 decimal places Centerline Upper Control Limit Lower Control Limit

A simple random sample of 90 is drawn from a normally distributed population and the mean is found to be 138 with a standard deviation of 34 What is the 90 confidence interval for the population mean Use the table below to help you answer the question Confidence Level Z score 90 1 645 O 128 75 to 147 25 O 130 98 to 145 02 O 132 10 to 143 90 O 137 38 to 138 62 95 1 96 Remember the margin of error ME can be determined using the formula ME Z S n 99 2 58

lect all that apply 1993 1994 1995 1996 United States 1997 United States United States United States United States United States United States United States United States United States United States United States Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity Animal waste Transformation in electricity 2003 185912 Terajoules 2002 197120 Terajoules 2001 104725 Terajoules 2000 126745 Terajoules 1999 133206 Terajoules 1998 224425 Terajoules 1997 129113 Terajoules ot the data to identify the potential outliers or examine the data For which years are outliers immediately evident from servation or fitting a line after calculation of linear equation 1996 5274 Terajoules 1993 21748 Terajoules 1992 242924 Terajoules 1991 210448 Terajoules 1990 215437 Terajoules

n 2011 there were 14 600 students at college A with a projected enrollment ncrease of 1000 students per year In the same year there were 35 600 students t college B with a projected enrollment decline of 500 students per year Complete parts a and b X 7 8 Y1 Y2 21600 32100 22600 31600 9 23600 31100 10 24600 30600 11 25600 30100 12 26600 29600 13 27600 29100 14 28600 28600 15 29600 28100 27600 16 30600 17 31600 27100 7 a According to these projections when will the colleges have the same enrollment What will be the enrollment in each college at that time According to these projections in the year 2025 the colleges will have the same enrollment and at that time 28600 students were enrolled Simplify your answers b Use the adjacent table to check your work in part a numerically Wha equations were entered for Y1 and Y2 to obtain this table Does the table check the work in part a numerically Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer OA Yes the answer checks because for x both the values in column Y1 and Y2 are the same and equal to the value found in part a OB No the answer does not check because for x both the values are in column Y1 and Y2 are different and the value found in part a is also different

During a bowling league tournament the number of times that teams scored a strike every ten minutes was recorded by a scorekeeper The table below represents the probability density function for the random variable X the number of strikes every ten minutes Find the standard deviation of X Round the final answer to two decimal places Provide your answer below X 0 3 4 8 P X X 1 6 1 6 1 3 1 3

The Social Security Administration documented the marriage year of various couples along with the number of children they had Use the table given below to answer the following One 1 Two 2 Three 3 Four or more 4 Total 1996 A 1997 B 1998 C 1999 D 2000 E Total 7 17 15 6 e Compute P En 4 5 50 c Compute P BUC n 2 d Compute P An E U 3 6 11 f Compute P B U D n 1 12 18 16 63 9 20 5 18 18 70 16 6 14 15 15 66 38 54 46 a If a couple is selected at random what is the probability the couple was married in 2000 and had two children 57 b If a couple is selected at random what is the probability the couple was married before 1998 or had three children 54 249

Use the given magic squares to complete part a and part b a Compute the sums of the numbers in each row column and diagonal of the square The sum of the top row is 7 20 18 26 15 4 12 10 23

The average home price in Massachusetts is 410 000 with a standard deviation of 65 000 A city planner is studying th distribution across the state of home prices in the bottom 10 What price will indicate that a home is in the bottom 10 the city planner examines 200 homes around the state Use the 2 table below 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 1 5 0 067 0 066 0 064 0 063 0 062 0 061 0 059 0 058 0 057 0 056 1 4 0 081 0 079 0 078 0 076 0 075 0 074 0 072 0 071 0 069 0 068 1 3 0 097 0 095 0 093 0 092 0 090 0 089 0 087 0 085 0 084 0 082 1 2 0 115 0 113 0 111 0 109 0 107 0 106 0 104 0 102 0 100 0 099 1 1 0 136 0 133 0 131 0 129 0 127 0 125 0 123 0 121 0 119 0 117 1 0 0 159 0 156 0 154 0 152 0 149 0 147 0 145 0 142 0 140 0 138 Round the z score oz and I to two decimal places Z score 1 28 Z Sorry that s incorrect Try again 4596 19 I

Quality control A population of 584 semiconductor wafers contains wafers from three lots The wafers are categorized by lot and by whether they conform to a thickness specification with the results shown in the following table A wafer is chosen at random from the population Write your answer as a fraction or a decimal rounded to four decimal places Lot A B C Conforming 82 156 253 Send data to Excel Nonconforming 17 45 31 a What is the probability that the wafer is from Lot C b What is the probability that the wafer is nonconforming c What is the probability that the wafer is from Lot C and is nonconforming d Given that the wafer is from Lot C what is the probability that it is nonconforming from Lot C e Given that the wafer is nonconforming what is the probability that it f Let E be the event that the wafer comes from Lot C and let E be the event that the wafer is nonconforming Are E and E independent TIT olo 11

7pm Points 100 Submitting an external tool Two swimmers Angie and Beth from different teams wanted to find out who had the fastest time when compared to her team Compute the scores for Angie and Beth Provide your answer below Angle Swimmer Time sec Team Mean Time Team Standard Deviation Angle 26 2 27 2 0 8 Beth 27 3 30 1 1 4

Between 1980 and 2012 the number of adults in a certain country who were overweight more than quadrupled from 14 to 58 Use this information to answer parts a and b 381 manu OA Percentage 1980 2012 60 50 G 1980 2012 Peni BOE Percentage B nan b Construct a misleading graphic that makes it appear that the percent of overweight adults has more than quintupled between 1980 and 2012 Choose the correct graph below 765432 Miniinisis WEEETTTww 1980 2012 L Pen 1980 2012 O C 99 00 Percentage 60 50 40 1980 20 10 0 2012 5 1980 2012 O D Percentage 1980 2012 65 45 1980 2012