Statistics Questions

The histograms each represent part of a binomial distribution Each distribution has the same probability of success p but different numbers of trials n Identify the unusual values of x in each histogram a n 4 b n 8 c n 12 AP x 0 5 0 44 0 3 0 2 0 1 0 0 1 2 3 4 5 6 7 8 9 10 Q E AP x 0 5 0 4 0 3 0 2 0 1 0 Fl 0 1 2 3 4 5 6 7 8 9 10 G AP x OA x 0 x 1 x 2 x 3 x 4 x 5 and x 6 OB x 0 x 1 x 2 x 3 and x 4 OC x 0 and x 1 OD There are no unusual values of x in the histogram 0 4 0 3 0 2 FL 0 1 0 ATAULAR 0 1 2 3 4 5 6 7 8 9 10111213 Identify the unusual values of x in histogram a Choose the correct answer below OA x 0 and x 1 OB x 3 and x 4 OC x 0 x 1 x 2 x 3 and x 4 D There are no unusual values of x in the histogram Identify the unusual values of x in histogram b Choose the correct answer below OA x 0 and x 1 OB x 7 OC x 0 x 1 x 2 x 3 and x 4 OD There are no unusual values of x in the histogram Identify the unusual values of x in histogram c Choose the correct answer below A

The following histograms each represent binomial distributions Each distribution has the same number of trials n but different probabilities of success p a P x 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 01234 c P x 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 01234 X X b P x 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 JL 01234 X Match p 0 3 p 0 5 p 0 6 with the correc graph OA a p 0 3 b p 0 5 c p 0 6 O B a p 0 5 b p 0 3 c p 0 6 OC a p 0 6 b p 0 3 c p 0 5 OD a p 0 3 b p 0 6 c p 0 5 OE a p 0 5 b p 0 6 c p 0 3 OF a p 0 6 b p 0 5 c p 0 3 4

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines The mean length of the conferences was 3 94 days with a standard deviation of 1 28 days Assume the underlying population is normal Determine an 95 confidence interval for the average length of ALL engineering conferences What Procedure would you use Select an answer 2 Sample T Interval Question Help Post to foru T Test Submit Question Jump t T Interval

A researcher wants to determine if students in the California state university system take longer to graduate than students enrolled in private universities One hundred students from the California state university system are surveyed and it is determined that they have a mean time to graduation of 5 7 years with a standard deviation of 1 5 years One hundred private university students are surveyed as well and their average time to graduation is 4 8 years with a standard deviation of 1 2 years Find an estimate to determine how much longer California state university students spend on average taking to graduate than private university students What Procedure would you use Select an answer 2 Sample T Interval Question Help Post to for 2 Sample T Test Submit Question Jump t 1 Proportion Z Test 2 Proportion Z Interval

eviously an organization reported that teenagers spent 4 5 hours per week on average on the phone The ganization thinks that currently the mean is higher Fifteen randomly chosen teenagers were asked how many hours r week they spend on the phone The sample mean was 4 75 hours with a sample standard deviation of 2 0 Does e organization have evidence to support their thought that the mean is currently higher at Procedure would you use Select an answer estion Help Post to foru ubmit Question Jump t 2 Proportion Z Interval 1 Proportion Z Test 2 Sample T Interval 2 Sample T Test

A camp director is interested in the mean number of letters each child sends during his or her camp session The population standard deviation is known to be 2 5 A survey of 20 campers is taken The mean from the sample is 7 9 Does the evidence show that campers on average send fewer than 10 letters during the camp session What Procedure would you use Question Help Post to foru Submit Question Jump t Select an answer 1 Proportion Z Test 1 Proportion Z Interval T Test 2 Sample T Interval

Ten individuals went on a low fat diet for 12 weeks to lower their cholesterol The data are recorded in the table below Does the evidence show that their cholesterol levels were significantly lowered Ending cholesterol level 140 230 120 220 190 150 220 300 300 240 Starting cholesterol level 140 220 110 240 200 180 190 360 280 260 S What Procedure would you use Question Help Post to foru Jump t Submit Question Select an answer Z Test 2 Sample T Test T Interval 2 Proportion Z Interval T Test

Effects of depression medication In clinical trials of the drug sertraline used for treating depression subjects were measured using the Hamiltonian depression scale with results given below Based on these results test the claim that the two population means are different Control 120 9 81 3 1 22 30 Treatment 19 3 82 3 8 7 30 The hypotheses for this test are O Ho Hcontrol Utreatment Ha Hcontrol treatment O Ho Hcontrol Utreatment Ha Pcontrol treatment x O Ho Hcontrol Htreatment Ha Hcontrol Htreatment m The p value is please round to three significant figures Interpret the result of the hypothesis test in the context of the problem O There is not sufficient evidence the means are different so we don t know if the medication has an effect There is not sufficient evidence that the means are the same and thus the medication may have an effect There is sufficient evidence the means are different and thus the medication has an effect There is evidence that the means are the same and thus the medication does not have an effect Use 2 SampTint to construct a 85 confidence interval for the difference between the population means please round to two decimal places

Military Test The Armed Services Vocational Aptitude Battery is multiple aptitude test battery used to assess the skills of applicants to the U S Armed Services A group of military officers are interested in comparing ASVAB scores for recruits for the Navy and Army Sample data from 200 Army recruits and 200 Navy recruits are collected and displayed below Test the claim that Navy applicants scores on average better than Army applicants The hypotheses for this test are O Ho Harmy Hnavy Ha Harmy Hnavy O Ho Harmy Hnavy Ha Harmy Unavy x O Ho Harmy Hnavy Ha Harmy Unavy Mean SD n Army Navy 52 4 56 0 20 4 24 2 200 200 The p value is please round to three significant figures Interpret the result of the hypothesis test in the context of the problem O There is not sufficient evidence that on average Navy recruit scores are the same as Army recruit scores There is not sufficient evidence that on average Navy recruit scores are better than Army recruit scores There is sufficient evidence that on average Navy recruit scores are the same as Army recruit scores O There is sufficient evidence that on average Navy recruit scores aro bottor

The effectiveness of a blood pressure drug is being investigated An experimenter finds that on average the reduction in systolic blood pressure is 43 5 mmHg millimeters of mercury for a sample of size 569 and a sample standard deviation 7 6 mmHg How much of mmHg will lower for a typical patient s systolic blood pressure after taking the drug Estimate with a 90 confidence Preliminary a Is it safe to assume that n 5 of all patients with a systolic blood pressure Yes O No b Is n 30 O No Yes Confidence Interval What is the 90 confidence interval to estimate the population mean Round your answer to one decimal place

A researcher must estimate the mean temperature in degrees Fahrenheit with the following sample temperatures 42 3 75 44 3 65 3 85 2 48 1 Assuming the population of temperatures are normally distributed find the 95 confidence interval Round the answers to two decimal places Enter your answer as an interval of the form LB UP The researcher is 95 confident that the population average temperature is within the temperature interval

We want to obtain a sample to estimate a population mean Based on previous evidence researchers believe the population standard deviation is approximately o 27 5 We would like to be 99 confident that the estimate is within 5 of the true population mean How large of a sample size is required n

Assuming the population has an approximate normal distribution if a sample size n 28 has a sample mean 30 with a sample standard deviation s 8 find the margin of error at a 99 confidence level Round the answer to two decimal places

Estimate the population mean by finding a 99 9 confidence interval given a sample of size 511 with a mean of 17 5 and a standard deviation of 9 8 Preliminary a Is it safe to assume that n 5 of all subjects in the population O No O Yes b Is n 30 O No OYes Confidence Interval What is the 99 9 confidence interval to estimate the population mean Enter the tri linear inequality values accurate to one decimal place

Use the following sample to estimate a population mean 85 75 9 94 7 72 3 75 3 87 9 72 2 80 7 95 9 76 Assuming the population is normally distributed find the 80 confidence interval about the populat mean Enter your answer as an open interval i e parentheses accurate to two decimal places 80 C I

A chemist has a 100 gram sample of a radioactive material He records the amount of radioactive material every week for 6 weeks and obtains the following data Complete parts a f Week x 0 1 2 3 4 5 6 Weight y in grams 100 0 82 7 66 5 56 9 45 3 37 2 30 5 Points 0 of 6 a Treating week x as the independent variable use a graphing utility to fit an expo function to the data y ab 100 4019 0 8204 Round to four decimal places as needed

For a confidence level of 80 with a sample size of 24 find the critical t value

A company producing computer components has established that on the average a new employee can assemble N t components per day after t days of on the job training as indicated in the following table a new employee s productivity usually increases with time on the job up to a leveling off point t N t 0 9 20 50 40 67 60 75 The regression equation is y Round to ten decimal places as needed 80 80 X 100 83 A Find a quadratic regression equation for the data and graph it and the data set in the same viewing window on your graphing calculator 120 84

ean value of land and buildings per acre from a sample of farms is 1700 with a standard deviation of 300 The data set has a bell shaped distribution Assume the number of in the sample is 75 se the empirical rule to estimate the number of farms whose land and building values per acre are between 1100 and 2300 arms Round to the nearest whole number as needed 30 additional farms were sampled about how many of these additional farms would you expect to have land and building values between 1100 per acre and 2300 per acre arms out of 30 Round to the nearest whole number as needed

A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red She estimates the probability model for the number of red lights she hits as shown below Complete parts a and b X of red P X x 0 1 0 04 0 24 2 0 34 3 0 15 a How many red lights should she expect to hit each day The commuter should expect to hit 2 4 red lights each day Round to one decimal place as needed b What s the standard deviation 4 0 15 5 0 08 D The standard deviation is Round the final answer to one decimal place as needed Round all intermediate values to three decimal places as needed

5 A teacher uses a program that randomly chooses a student in the class to volunteer to answer a question The teacher will stop choosing students once a student gets the right answer but if the teacher is given four wrong answers in a row he will stop and help the class himself He estimates that 82 of the students in the class know the correct answer Assume that students are chosen with replacement Complete parts a through c below a Create a probability model for the number of students the teacher will call on until he receives the correct answer or stops to help the class Number of students 1 3 4 Probability Type integers or decimals Do not round b Find the expected number of students called on 2 The expected number of students called on is Round to two decimal places as needed c Find the expected number of wrong answers that will be offered The expected number of wrong answers offered is Round to two decimal places as needed

The data in the table below represents the percentage of patients who have survived after diagnosis of advanced stage breast cancer at 6 month intervals of time Time after Diagnosis years 0 5 1 1 5 2 2 5 3 3 5 Percentage Surviving 94 1 82 4 74 0 58 9 46 3 40 4 33 2 b Express the function found in part a in the form A t Aekt where t x 0 3585 t A t 117 9568 e Type integers or decimals rounded to four decimal places as needed c Draw a scatter diagram of the data with the time after diagnosis as the independent variable Graph the exponential function found in part a or b on the scatter diagram Choose the correct graph below Use the graphing window 0 5 1 x 0 100 10 OA OC Q Q OB D SOU Q d What percentage of patients diagnosed with advanced stage cancer are expected to survive for 4 years after the initial diagnosis About of patients are expected to survive for 4 years after the initial diagnosis oc pooded

It is widely accepted that people are a little taller in the morning than at night Here we perform a test on how big the difference is In a sample of 35 adults the mean difference between morning height and evening height was 5 5 millimeters mm with a standard deviation of 1 59894 mm Test the claim that on average people are more than 5 mm taller in the morning than at night Test this claim at the 0 05 significance level a Find the test statistic b Find the critical value 0 c Is there sufficient data to support the claim O Yes No

3 A popular restaurant in the mall has conducted market research on four new salads it is considering putting on the menu The percentages of study participants in various age categories and their salad preferences are shown in the table below Salad preference was found to be independent of age Salad preference Feta Cheese 10 BBQ Chicken 60 Asian Ginger 10 Chopped Cobb 20 Under 25 36 25 to 34 14 35 to 44 17 Age 45 to 54 14 55 to 64 8 65 to 74 6 75 and over 5 a People who participated in the study will be randomly selected for face to face interviews What is the probability that the marketing department will randomly select someone who is 55 or older and prefers the BBQ chicken salad b Is the event you analyzed in part a an intersection or a union How does the intersection of 55 or older and BBQ differ from the union of 55 or older and BBQ c Calculate the probability of 55 or older or BBQ using the Addition Rule How does it compare to the probability from part a 3 What is the probability that a randomly selected person from the study is under 75 years old

6 A small software company bids on two contracts It anticipates a profit of 40 000 if it gets the larger contract and a profit of 20 000 if it gets the smaller contract The company estimates that there is a 34 chance it will get the larger contract and a 62 chance it will get the smaller contract If the company does not get either contract it will neither gain nor lose money Assuming the contracts will be awarded independently what s the expected profit E X

In which of the following scenarios will conducting a paired t test for means be appropriate CHECK ALL THAT APPLY OA To test if the proportion of low income families is higher than that of high income families in British Columbia OB To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery Oc To test if there is a difference between the mean annual income of husbands and that of their wives in Canada D To test if the mean annual income of Ontarians is higher than that of British Columbians OE To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer OF To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians OG None of the above

Two samples are taken with the following sample means sizes and standard deviations T1 27 T 31 n 71 7 73 81 4 8 5 Estimate the difference in population means using a 99 confidence level Use a calculator and choose NO for pooled Round answers to two decimal places 1 2

Given the dimensions of the WGS 84 Ellipsoid A 6 378 137 meters f 1 298 257223563 Compute the radius of curvature in the prime vertical No for stations P Hint e 2f f2 and see data below Station P Q 40 44 29 N 39 46 52 N O 3698754 63 m 8945876 36 m 074 10 40 W 075 07 11 W Geodetic Height h 17 929 m 3 984 m

8000 7900 7800 7700 7600 7500 7400 7300 7200 7100 7000 012 2013 2014 2015 2016 2017 2018 2019 202 6900 2014 Factory Line I Truckload Output by Year To the nearest hundred a Estimate the number of Factory Line 1 Truckload Output for the year 2014 b Estimate the number of Factory Line 1 Truckload Output for the year 2018 c Find the year with the greatest output year d Find the year with the least output year What was the approximate Truckload Output for the What was the approximate Truckload Output for that

2 This recent study was conducted in a school fitness class interviewing 100 students To examine how drinking water relates to how well people sleep in this specific fitness class consider the following table 2 a Sleep 28 hours Sleep 8 hours Total Drink 2 64 oz of Water 40 Drink 64 oz of Water If a student in the fitness class was chosen at random P Drink 2 64 oz n Sleep 28 hours 30 2 b If a student in the fitness class was chosen at random P Sleep 28 hours Drink 64 oz Total 50 100 What is the probability that a randomly chosen person either drinks less than 64 oz of water per day or gets less than 8 hours of sleep at night Given that a randomly chosen person gets less than 8 hours of sleep at night what is the probability that this person drinks at least 64 oz of ater per day

Samples of pages were randomly selected from the three books The mean number of words per sentence was computed for each page and the analysis of variance results from some statistical software are shown below Using a 0 05 significance level test the claim that the three books have the same mean number of words per sentence The mean number of words per sentence taken from samples of pages that were randomly selected from three books Source DF WORDS 2 Error Total 33 SS MS 266 5 133 3 1123 7 34 1 35 1390 3 F 3 91 P 0 030 O There is not sufficient evidence to support the claim that the three books have the same mean number of words per sentence O There is not sufficient evidence to warrant rejection of the claim that the three books have the same mean number of words per sentence

Do male and female servers at Swank Bar work the same number of hours A sample of 45 female servers worked an average of 35 hours per week with a standard deviation of 2 A sample of 45 male servers worked an average of 20 hours per week with a standard deviation of 3 Let and 2 represent the typical number of hours worked by all female and male servers at Swank Bar respectively Estimate with a 98 confidence level how many more hours female servers work Round answers to the nearest hundredth 1k2 Which of the following does your data suggest O Female and male servers work about the same number of hours Female servers work more hours Male servers work more hours

Records of randomly selected births were obtained and categorized according to the day c the week that they occurred based on data from the National Center for Health Statistics Because babies are unfamiliar with our schedule of weekdays a reasonable clai is that births occur on the different days with equal frequency Use a 0 01 significance lev and find the test statistic for a Goodness of Fit test and the critical value Records of randomly selected births by the day of the week Sun Mon Tues Wed Thurs Day Number of Births 77 110 124 122 O Test statistic x 16 895 Critical value x 18 475 O Test statistic x 17 124 Critical value x 16 812 O Test statistic x 17 124 Critical value x 18 475 2 1 005 Critical voluer 2 16812 120 Fri Sat 123 97

8000 7900 7800 7700 7600 7500 7400 7300 7200 7100 7000 012 2013 2014 2015 2016 2017 2018 2019 202 6900 Factory Line I Truckload Output by Year To the nearest hundred a Estimate the number of Factory Line 1 Truckload Output for the year 2014 b Estimate the number of Factory Line 1 Truckload Output for the year 2018 c Find the year with the greatest output year d Find the year with the least output year What was the approximate Truckload Output for t What was the approximate Truckload Output for that

domly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred and the results are listed below based on data from the Bureau of Labor and Statistics Use a 0 05 significance level to test the claim that such injuries and illnesses occur with equal frequency on the different days of the week Randomly selected nonfatal occupational injuries and illnesses by the day of the week Mon Tues Wed Day Number 23 23 21 Thurs 21 Fri 19 O There is sufficient evidence to warrant rejection of the claim that injuries and illnesses occur with equal frequency on the different days of the week O There is not sufficient evidence to support the claim that injuries and illnesses occur with equal frequency on the different days of the week O There is not sufficient evidence to warrant rejection of the claim that injuries and illnesses occur with equal frequency on the different days of the week

Randomly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred and the results are listed below based on data from the Bureau of Labor and Statistics Use a 0 05 significance level and find the test statistic for a Goodness of Fit test and the critical value Randomly selected nonfatal occupational injuries and illnesses by the day of the week Mon Tues Wed Thurs Fri Day Number 23 23 21 21 O Test statistic x 0 478 Critical value x 9 488 O Test statistic x 0 478 Critical value x 11 071 O Test statistic x 0 523 Critical value x 9 488 19

3 Police trainees were seated in a darkened room facing a projector screen Ten different license planes were projected on the screen one at a time for 5 seconds each separated by 15 second intervals After the last 15 second interval the lights were turned on and the police trainees were asked to write down as many of the 10 license plate numbers as possible in any order at all A random sample of 10 trainees who took this test where then given a week long memory training course They were then retested The results are shown in the table below X Person a 1 pt What are the Ho and HA 1 2 3 4 5 6 7 8 9 10 After Training 6 8 6 7 5 9 8 6 5 4 Do these results provide evidence that the memory course improved the ability of the trainees to correctly identify license plates Use a 0 05 level of significance Use After Before X2 Before Training b 1 pt What is the P Value Round to 4 decimal places 4 7 5 5 8 7 6 5 4 2

The amounts in millions of dollars grossed by movies in categories with PG PG 13 anc ratings we obtain the analysis of variance results from statistical software below Using 0 05 significance level find the test statistic F and the critical value of F The amounts in millions of dollars grossed by movies in categories with PG PG 13 and R ratings Between Groups Within Groups Total Sum of Squares df 84801 867 255396 1 2 41 340198 0 43 Mean Squares F 42400 933 5 313 7981 129 O Test statistic F 5 313 Critical value of F is approximately 3 23 O Test statistic F 5 313 Critical value of F is approximately 0 87 Test statistic F 5 313 Critical value of F is approximately 7 43 Sig 010

Samples of pages were randomly selected from the three books The mean number of words per sentence was computed for each page and the analysis of variance results from some statistical software are shown below Using a 0 05 significance level find the test statistic F and the critical value of F The mean number of words per sentence taken from samples of pages that were randomly selected from three books Source DF WORDS 2 SS MS 266 5 133 3 3 91 Error 33 1123 7 34 1 Total 35 1390 3 F P 0 030 O Test statistic F 3 91 Critical value of F is approximately 6 56

Chantix is a drug used as an aid for those who want to stop smoking The adverse reaction of nausea has been studied in clinical trials and the table below summarizes the results based on data from Pfizer Use a 0 01 significance level to find the test statistic for a test of independence and the critical value Adverse reactions caused by Chantix Placebo Chantix Nausea No nausea 10 795 30 791 O Test statistic x 9 854 Critical value x 9 210 O Test statistic x 7 119 Critical value x 9 210 O Test statistic x 7 119 Critical value x 6 635

In the 2005 World Series the Houston Astros wanted to close the roof on their domed stadium so that fans could make noise and give the team a better advantage at home However the Astros were ordered to keep the roof open unless weather conditions justified closing it But does the closed roof really help the Astros The table below shows the results from the home games during the season leading up to the World Series Use a 0 05 significance level to find the test statistic for a test of independence and the critical value Results from the home games during the season leading up to the World Series for the Astros Win Loss Closed roof 36 Open roof 15 17 11 OF O Test statistic x 0 798 Critical value x 5 024 Test statistic x 0 697 Critical value x 5 024 Test statistic y 0 697 Critical value y 3 841

Below is data obtained from randomly selected crime victims based on data from the U S Department of Justice And below the table are the results of some statistical software What can we conclude from the software results Data obtained from randomly selected crime victims Homicide Robbery Assault 12 379 727 Criminal was a stranger Criminal was acquaintance or relative 39 106 642 Statistical Software Results x 119 330 DF 2 P Value 0 000 UP O We can make no conclusions because the observed frequencies conflict with the test statistic O We can make no conclusions because the observed frequencies conflict with the critical value O Fail to Reject the null hypothesis that the type of crime is independent of whether the criminal is a

2 Suppose Netflix conducts a nation wide survey to assess viewer habits regarding the show Ozark Using a simple random sample they select 8 000 men and 6 500 women to participate in the study 7 102 of the men say that they watch Ozark compared to 4 817 of the women a 1 pt Estimate the difference in viewing habits of Ozark using a 95 confidence interval b 2 pts Write a real world interpretation of this problem

1 We want to see if there is a difference in the average delivery time of two local pizza restaurants To check this we ordered pizza 6 different times from both restaurants controlling for time of day weather and traffic The average delivery time for pizza place A was 29 1 minutes with a standard deviation of 1 minute and for place B it was 26 5 minutes with a standard deviation of 1 2 minutes a 1 pt Estimate the difference in delivery times with a 95 confidence interval Round to 4 decimal places b 2 pts Write a real world interpretation of this problem

Lower Limit 9 98064 Upper Limit 40 71402 2 A local fisherman claims that the proportion of large fish over 350 grams i e 3 4 of a pound river was higher in 2000 than in 2006 Is there statistical evidence to support or refute his claim You want to add a column of data for size and fill it with the words large and small To do this an i statement can be quite efficient For example IF D2 350 large small will determine whether a weight is over 350 and assign it the word large if so Then pull this command down or double click the lower right corner of the cell to fill in all the large small decisions Include both sections of the riv both years a Clearly state your hypotheses

A study of working actors looked at age and gender One sample of 55 male actors had a mean age of 20 and a standard deviation of 3 The other sample included 55 female actors with a mean age of 38 and a standard deviation of 2 Estimate with 95 confidence the difference between the average ages of working male and female 2 actors Round answers to the nearest hundredth 1 1 Question Help Post to forum Submit Question

Give a 99 8 confidence interval for 1 2 given the following information n 60 1 2 17 s1 0 66 n2 50 T 1 73 s2 0 71 Hint H Use Technology Rounded to 2 decimal places

Find the values of the slope m and the y intercept b for the line y mx b graphed below 7 6 5 7 6 54 3 The slope is m The y intercept is b 7 4 32 1 2 5 6 7 1 2 3 4 5 6 a This does not need to be written as an ordered pair

Write the equation of the line with a slope of 5 and a y intercept of 1 Y

Determine the slope and y intercept of the graph of the linear equation y 7x 1 Slope y intercept