Statistics Questions and Answers

Past studies have indicated that the percentage of smokers was estimated to be about 34 Given the new smoking cessation programs that have been implemented you now believe that the percentage of smokers has reduced You randomly surveyed 2268 people and found that 717 smoke Use a 0 05 significance level to test the claim that the percentage of smokers has reduced a Identify the null and alternative hypotheses Ho H H b What type of hypothesis test should you conduct left right or two tailed Oleft tailed Oright tailed Otwo tailed c Identify the appropriate significance level d Calculate your test statistic Use p rounded to 4 decimal places Write the result below and round your test statistic to 4 decimal places Calculate your p value Write the result below rounded to four decimal places

A political candidat assume p 5 If the candidate on

13 Studies have found that people find symmetrical faces more attractive than faces that are not symmetrical To test this theory a psychiatrist selected a random sam ple of people and showed them pictures of three different faces a face that is per fectly symmetrical a face that is slightly asymmetrical and a face that is highly asymmetrical She then asked them to rate the three faces in terms of their attrac tiveness on a scale from 1 to 7 with 7 being the most attractive a Test the null hypothesis that attractiveness does not differ with facial sym metry Symmetrical 6 7 5 6 6 Slightly Asymmet Highly Asymmet rical rical 5 4 5 2 4 5 I 2 3 1 1 22

CHOROSCO Number of hits at a baseball tournament 30 25 20 15 10 5 0 1st place 11 2nd 3rd place place Based on the bar graph above which of the following conclusions is true O The third place team had at least 20 hits The second place team had half as many hits as the first place team There was more than a 5 hit difference between the first and third place team The third place team had 20 hits

ed information llowing information applies to the questions dis ompany prepared the following contribution for evant range of production is 500 units to 1 500

8 In Problem 1 19 we noted that the Wright brothers in the design of their 1900 and 1901 gliders used aerodynamic data from the Lilienthal table given in Figure 1 65 They chose a design angle of attack of 3 degrees corresponding to a design lift coefficient of 0 546 When they tested their gliders at Kill Devil Hills near Kitty Hawk North Carolina in 1900 and 1901 however they measured only one third the amount of lift they had originally calculated on the basis of the Lilienthal table This led the Wrights to question the validity of Lilienthal s data and this cast a pall on the Lilienthal table that has persisted to the present time However in Reference 58 this author shows that the Lilienthal data are reasonably valid and that the Wrights misinterpreted the data in the Lilienthal table in three respects see pages 209 216 of Reference 58 One of these respects was the difference in aspect ratio The Wrights 1900 glider had rectangular wings with an aspect ratio of 3 5 whereas the data in the Lilienthal table were taken with a wing with an ogival planform tapering to a point at the tip and with an aspect ratio of 6 48 The Wrights seemed not to appreciate the aerodynamic importance of aspect ratio at the time and even if they had there was no existing theory that would have allowed them to correct the Lilienthal data for their design Prandtl s lifting line theory appeared 18 years later Given just the difference in aspect ratio between the Wrights glider and the test model used by Lilienthal what value of lift coefficient should the Wrights have used instead of the value of 0 546 they took straight from the table Note There are two other misinterpretations by the Wrights that resulted in their calculation of lift being too high see Reference 58 for details

1 Define the term statistically significant in terms of your text s usage 2 Define the term test statistic 3 Define the term p value 4 Is a p value the probability that the null is true 5 Is a p value the probability of rejecting the null 6 When our p value is less than the significance level we say we reject the null and accept the alternative Why do we NOT say we accept the null if our p value is greater than the significance level

7 Glaxco claims that its new sleeping pill Somatripan has a mean time of entering the bloodstream of less than 10 min What should the null hypothesis be The alternate hypothesis Glaxco reports the results of the test have a p value of 004 The FDA requires a 005 level of significance for tests of new drugs Will the FDA approve Glaxco s drug

Transcribed image text TABLE B 1 National Football League 1976 Team Performance y 10 11 11 X1 2113 2003 2957 X2 1985 2855 1 737 X3 38 9 38 8 40 1 X4 64 7 61 3 60 0 X5 4 3 14 X6 868 615 914 X 59 7 55 0 65 6 X 2205 2096 1847 X 1917 1575 2175 2971 11 Team Washington Minnesota New England Oakland Pittsburgh Baltimore Los Angeles Dallas Atlanta Buffalo Chicago Cincinnati Cleveland Denver Detroit Green Bay Houston Kansas City Miami New Orleans New York Giants New York Jets Philadelphia St Louis San Diego San Francisco Seattle Tampa Bay 132285 10 2309 10 2528 11 2147 4 1689 2 2566 2363 10 2109 92295 9 1932 6 2213 5 1722 5 1498 5 1873 6 2118 4 1775 2905 1666 2927 2341 2737 1414 1838 1480 2191 2229 2204 2140 1730 2072 2929 2268 1983 41 6 39 2 39 7 38 1 37 0 42 1 42 3 37 3 39 5 37 4 35 1 38 8 36 6 35 3 41 1 38 2 39 3 45 3 53 8 74 1 65 4 78 3 47 6 54 2 48 0 51 9 53 6 71 4 58 3 52 6 59 3 55 3 69 6 78 3 dooto 4957 61 4 15 836 66 1 8 786 61 0 12 754 66 1 761 58 0 3 714 57 0 1 797 58 9 19 984 67 5 6 700 57 2 5 1037 58 8 3 986 58 6 6 81959 2 19 791 54 4 5 776 49 6 19032476 1457 1866 1848 2339 1564 2092 1821 1909 2577 2001 2476 2254 1984 2217 1917 1758 1761 2032 1709 2025 1901 1686 2288 1835 2072 1914 2861 2496 2411 2670 2289 2202 6 7 582 901 58 7 51 7 2592 52 7 627 68 8 39 7 1606 1929 L 1988 2203 61 9 734 38 1 39 7 1792 1904 L 50 74 1 68 8 39 9 7 38 35 3 35 5 638 1 2416 2835 1492 2447 2040 2301 2080 86 10 4 2 8 2324 028 1776 2628 2110 2550 1786 2048 1979 2053 65 3 54 9 59 7 57 8 848 576 683 722 0 57 1 0 2241 2524 2560 2876 53 5 43 8 875 684 9 22 47 0 56 3 39 3 37 4 1503 2649 1503 1416 y Games won per 14 game season xi Rushing yards season xz Passing yards season xz Punting average yards punt x4 Field goal percentage FGs made FGs attempted 2season xs Turnover differential turnovers acquired turnovers lost x6 Penalty yards season X Percent rushing rushing plays total plays Xg Opponents rushing yards season Xg Opponents passing yards season

8 A surgical team claims that their new procedure has a mean recovery time that is shorter than the existing procedure of 3 days What should the null hypothesis be The alternate hypothesis In their paper they quote that the results of their analysis has a p value of 0 03 At what value of alpha below would this be a significant result Would the claim then be accepted 001 a b 005 C 01 d 025 e 05

98 A sample of 16 small bags of the same brand of candies was selected Assume that the population distribution of bag weights is normal The weight of each bag was then recorded The mean weight was two ounces with a standard deviation of 0 12 ounces The population standard deviation is known to be 0 1 ounce ii iii x b In words define the random variable X c In words define the random variable X d Which distribution should you use for this problem Explain your choice e Construct a 90 confidence interval for the population mean weight of the candies i State the confidence interval ii Sketch the graph iii Calculate the error bound f Construct a 98 confidence interval for the population mean weight of the candies i State the confidence interval ii Sketch the graph iii Calculate the error bound g In complete sentences explain why the confidence interval in part f is larger than the confidence interval in part e h In complete sentences give an interpretation of what the interval in part f means

8 What is the statistical symbol for the slope of the regression line For this problem its value is Use a completa sentence to write an interpretation of the slope in context of the problem 9 What is the statistical symbol for the y intercept of the regression line value is problem For this problem its Use a complete sentence to write an interpretation of the y intercept in context of the 10 What is the symbol for the correlation coefficient of the regression line For this problem its value is Use a complete sentence to write an interpretation of the correlation coefficient in context of the problem 11 What is the symbol for the coefficient of determination of the regression line its value is Use a complete sentence to write an interpretation of the coefficient of determination in context of the problem For this problem 12 Use your calculator to create a residual plot of the data Sketch it below Then describe what you see in complete sentences Is a line a best fit for the data

The probability distribution for the number of students in Statistics classes offered at a small college is given but one value is missing Fill in the missing value then answer the questions that follow P X X 26 0 17 27 0 21 28 0 24 29 30 0 19 Find the mean number of students in a Statistics class at the college Find the standard deviation of the number of students in a Statistics class at the college

0 11 0 24 0 11 0 16 0 31 0 07 2 4 6 7 9 11 Find the expected value of the above random variable

An online streaming service that offers TV shows documentaries and movies charges an initial fee of 20 25 and an additional monthly membership fee of 3 75 The total cost N f for a member after t months can be expressed with the function N t 3 75t 20 25 What is the range of the function in the context of the problem OR 0 0 00 O 3 75 00 012035 BY

Porter is visiting India and would like to purchase some local spices He finds some spices that cost 320 38 rupees If the current exchange rate is 1 dollar 73 6500 rupees how much do the spices cost in U S dollars O 0 04 O 4 35 O 22 99 O 23 595 99

Mikaela purchased a paddleboard originally priced at 699 If all merchandise was on sale for 40 off and the state tax rate is 7 25 what is the total amount that Mikaela spent on the paddleboard 449 81 470 08

Which of the following expressions is equivalent to 2 x 4 of 8 03 0 4

Quincy has a jewelry business in which he designs and sells bracelets His daily profit Q x can be modeled by the function Q x 8 25x 24 75 where x is the number of bracelets he sells What is the value of Q 3 and what is its interpretation Q 3 0 If Quincy sells 3 bracelets he will earn 0 Q 3 0 If Quincy sells 0 bracelets he will earn 3 O Q 3 3 36 If Quincy sells 3 bracelets he will earn 3 36 O Q 3 3 36 If Quincy sells 3 36 bracelets he will earn 3

An event manager is tracking participation in a tournament by age group The manager created the following histogram Number of People 60 50 40 30 20 10 0 O 10 0 19 20 39 40 59 60 79 Age Group yr What percentage of the tournament participants are under the age of 20 Round to the nearest whole percent 23 Tournament Participants 30 077

Electric circuit boards are rated excellent acceptable or unacceptable Suppose that 30 of boards are excellent 60 are acceptable and 10 are unacceptable Further suppose that 10 of excellent boards fail 20 of acceptable boards fail and 90 of unacceptable boards fail a What is the probability that a board fails b Given that a board fails what is the probability that it was rated excellent

The median home value in South Carolina and Washington adjusted for inflation are shown below Year South Carolina 1950 2000 31000 94900 Washington 43400 168300 If we assume that the house values are changing linearly a In which state have home values increased at a higher rate Washington b If these trends were to continue what would be the median home value in South Carolina in 2010 c If we assume the linear trend existed before 1950 and continues after 2000 the two states

The probability distribution for a random variable x is given in the table 10 5 0 5 10 15 20 Probability 20 15 05 1 25 1 15 X

n a test for the difference between two proportions the sample sizes were n 119 and 80 and the numbers of events were x 64 and X 35 test is made of the hypotheses Ho P P versus H P P2 Part 0 3 Part 1 of 3 a Compute the P value using your calculator Round your answer to four decimal places The value ic

amples come from populations that are approximately normal Let denote the mean weight of boys Can you conclude that the mean weight of boys is les han the mean weight of girls Use the a 0 01 level and the P value method with the TI 84 Plus calculator 5 9 6 4 7 3 6 6 6 9 6 3 6 4 6 4 7 4 7 7 Girls 7 7 7 0 8 2 7 4 6 0 6 7 8 2 7 5 5 7 6 6 6 4 8 5 7 2 6 9 6 2 Send data to Excel Part 0 4 Part 1 of 4 State the null and alternate hypotheses Ho H Boys 7 6 7 5 6 9 7 4 6 4 0 0 0 0 Hi

nterpret calculator display The following TI 84 Plus calculator display presents the results of a hypothesis test for the difference between two means ample sizes are n 22 and n 29 2 SampTTest 1 1 t 1 648010462 p 947056524 df 47 96325246 x 3 9001 x 5 1231 Sx 2 46455775 Sx 2 82210259 Part 0 4 Part 1 of 4

Finding t What critical value t from Table T 3 should be used in constructing a confidence interval for the population mean in each of the following settings Assume the conditions are met a A 95 confidence interval based on n 10 randomly selected observations b A 90 confidence interval based on a random sample of 77 individuals Round your answers to three decimal places

Mineral loss during nursing Breast feeding mothers secrete calcium into their milk Some of the calcium may come from their bones so mothers may lose bone mineral Research measured the percent change in bone mineral content BMC of the spines of 47 randomly selected mothers during three months of breast feeding The mean change in BMC wa 3 587 and the standard deviation was 2 506 Determine if the conditions for calculating a confidence interval for mean are met in each of the following settings A Random Select B Normal Select C Independent Select

What can be said of the correlation between the brand of an automobile and its quality The correlation is negative because smaller cars tend to have higher quality and larger cars tend to have lower quality Correlation makes no sense here because brand is a categorical variable If the correlation is negative an arithmetic mistake was made correlation must be positive The correlation is positive because better brands have higher quality

An economist conducted a study of the possible association between weekly income and weekly grocery expenditures The particular interest was whether higher income would cause shoppers to spend more on groceries A random sample of shoppers at a local supermarket was obtained A questionnaire was administered asking about the weekly income of each shopp family and their grocery bill for that week The gender of each shopper was also obtained The relationship between grocery expenditure and income was assessed by calculating both a correlation for the females only and a correlation for the males only For the females r 0 45 and for the males r 0 38 We conclude that there is not enough information to determine which gender has a stronger relationship between grocery expenditures and income the relationship between grocery expenditures and income is stronger for females the relationship between grocery expenditures and income is stronger for males the relationship between grocery expenditures and income is the same for males and females

C The following is a scatterplot of the liters of alcohol from drinking wine per person and the death rates from heart disease per 100 000 people for each of 19 countries The least squares regression line has been drawn in on the plot 150 D 2 50 260 9 Akebel from Dreking Wine Based on the least squares regression line we would predict that in a country where per person 7 liters of alcohol from wine is consumed the death rate from heart disease per 100 000 people would be about O 100 O 700 C O

5 points Suppose the least squares regression line for a set of data has slope 72 4 Now suppose we remove a point from the data compute the least squares regression line and find that the new slope is 8 7 The point removed would be considered a residual O O a response influential robust

The data and the graph below show the scores students in an advanced statistics course received for homework Hw completed and for the subseque based on assignments that preceded the exam The maximum homework score a student could obtain was 500 and the maximum midterm score was 350 51 Homework scores vs exam scores 280 459 Hw 275 387 score Exam 190 200 108 score The slope for the regression line is 0 84 0 84 0 91 323 395 314 315 256 428 341 366 421 236 285 234 125 am

According to the 2010 census those states with an above average number of people who fail to complete high school X tend to have an above average number of infant deaths Y In oth words there is a positive association between X and Y The most plausible explanation for this association is that lurking variables are probably present For example states with large populations will have both a larger number of people who fail to complete high school and a larger number of infant deaths X causes Y Thus programs to keep teens in school will help reduce the number of infant deaths the association between X and Y is purely coincidental It is implausible to believe the observed association could be anything other than accidental Y causes X Thus programs that reduce infant deaths will ultimately reduce the number of high school dropouts

A researcher measures the correlation between two variables This correlation tells us whether a scatterplot shows an interesting pattern whether a cause and effect relation exists between two variables the strength and direction of a linear association between two variables whether there is a relation between two variables

The volume of oxygen consumed in liters per minute while a person is at rest and while a person is exercising running on a treadmill were both measured for 50 subjects The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest The results are plotted below Volume Consumed While Ring 5 5 5 0 13 0 1 02 increase 03 0 4 0 5 Volume Consumed at Rest 06 0 7 If the outlier is removed the correlation coefficient will decrease There is not enough information to determine the effect on r neither increase nor decrease

A researcher states that bone density in women is negatively associated with age This means that older women aren t any more likely than younger women to have below average bone density below average values of age tend to accompany below average values of bone density as women get older bone density tends to decrease as women get older bone density tends to increase

Step 1 Sketch the star polygon for each set of points containing the number of star point vertices ranging from 3 to 11 and k the count between points connected by a segment ranging from 1 to 10 Either create your own table for your set of star polygons or use the table provided for you by your teacher Look for patterns 4 6 10 11 Step 2 Did you notice any duplicates in the rows What symmetries dia you find State a rule for when two star polygons are the same Step 3 What did you notice about the n and k for the star polygons that are just convex polygons Step 4 What did you notice about the n and k for the asterisk star polygona Step 5 What did you notice about then and k for the star polygons that were two or more overlapping triangles Step 6 Were there any star polygons that were made up of overlapping quadrilaterals or overlapping pentagons What was the relationship between them and k for these star polygons Step 7 What type of star polygon is 20 10 or 20 4 or 20 15 or 20 11 Explain your reasoning on is equivalent to a 20 10 or 20 4 or 20 15 or 20 11

fixed expenses grants car insurance nonsufficient funds cover letter fee schedule bonds portfolio capital gains PIN Personalidentification Number Resume diversification realestate budget surplus benefits bank statement checking account health insurance identity theft capital losses bull market bear market liquidity credit union volatility fraud mutual funds budget variable expenses stocks beneficiary savings account scholarships safe deposit box Federal Trade Commission FTC dividends asset allocation APY Annual Percentage Yield overdraft overdrawing budget deficit 1 2 3 When the stock market is trending downward Expenses that may increase or decrease from month to month yaxialble expenses A kind of investment made up of a group of securities stocks or bonds The fund is created and managed by a business with the intention of increasing profits and returns for the fund s shareholders 4 Money for education given to a student based on criteria such as academic ability or athletic skill schebychips 5 An office of the government responsible for consumer protection They deal with cases like identity theft credit card mistreatment and fraudulent sales schemes ETC Distributing investments among different asset classes Stocks bonds options mutual funds CDs T bills etc are examples of different classes of assets 6 7 A complete list of fee charges on bank accounts Banks are mandated to create and provide these schedules to customers by the Truth in Savings Act 8 Intentional deceit for the purpose of gain 9 A contract between you and the insurance company that protects you against financial loss in the event of an accident or theft In exchange for your paying a premium the insurance company agrees to pay your losses as outlined in your policy 10 The percentage interest payments on a bank account on a yearly basis The Truth in Savings Act of 1991 required that banks calculate and demonstrate to consumers a standardized APY for an account so that various accounts are directly comparable 11 A way of managing the financial risks of getting sick or injured In exchange for a monthly fee called a premium the insurance will pay for hospital medical and drug costs 12 Negative returns on an investment that involve selling the asset for less than was paid for it 13 A personal career document outlining professional job history and experience which highlights abilities and education Resume

Construct a 95 confidence interval for the difference in means from the two locations O 2 40 9 60 O 4 573 7 427 O 2 539 9 461 O 6 235 18 235 O 3 228 8 772

http www mathsisfun com data quincunx html Page 3 In the simulator create a quincunx with 8 rows of pegs and with a 50 chance of bouncing left and a 50 chance of bouncing right each time a marble strikes a peg a Click restart and let exactly 20 marbles fall Click pause the moment 20 is shown Convert the number of marbles in each bin to a probability So divide each number by the total number of marbles Then enter the probabilities into this table rounding each to 3 decimal places 0 1 2 Xx P x 3 4 3 LO 5 4 P x b Now let exactly 100 marbles fall Convert the number of marbles in each bin to a probability Round to 3 decimal places 0 1 2 3 4 5 6 5 6 7 6 c Lastly let exactly 500 marbles fall Convert the number in each bin to a probability Round to 3 decimal places X 0 1 2 P x d Compare the three distributions above Which of the three do you believe best models the actual probabilities of these bins In other words which best models the probabilities according to the Law of Large Numbers AMA 7 8 7 8 3 8 of 3 Copy and paste it in your browser and it should come up I apologize for the hassle Please type the answer

in 2008 the per capita consumption of soft drinks in Country A was reported to be 18 18 gallons Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed with a mean of 18 18 gallons and a standard deviation of 5 gallons Complete parts a through d below KER a What is the probability that someone in Country A consumed more than 13 gallons of soft drinks in 2008 The probability is 0 8499 Round to four decimal places as needed b What is the probability that someone in Country A consumed between 1 and 7 gallons of soft drinks in 2008 The probability is Round to four decimal places as needed

QUESTION 1 hospital administrator wante cords ear umber of Admissions

ESTION 4 particular relationship N 80 How many point ession line 0 30 4

State Alaska Arkansas Colorado Connecticut Delaware Idaho Indiana lowa Maine Missouri Montana Nebraska New Jersey New York Ohio Exercise Time mins Life Expectancy years 48 0 78 9 30 0 75 6 70 0 79 5 73 0 80 1 45 0 77 8 61 0 34 0 59 0 47 0 39 0 48 0 52 0 71 0 75 0 33 0 79 1 76 8 79 1 78 4 77 0 78 8 79 0 79 6 80 3 76 6

ESTION 6 regression constant for predicting Y Y

STION 8 near regression analysis to predict the Midt

Perform a linear regrssion analysis on this data Then pred Match each statistic with its value The coefficient of determination The predicted daily rating of a day where 25 people we the front subway car The slope of the best fit line used to predict rating The intercept of the best fit line used to predict rating The correlation coefficient z y xy

QUESTION 2 S Y Y equals 0 1 cannot be determined from information gi who cares QUESTION 3 If the relationship between X and Y is perfect Or by O2 1 wwwww

Noise levels at 6 airports were Construct the 80 confidence Step 1 of 4 Calculate the came