Statistics Questions and Answers

2 points The arrival of patients to a pharmacy can be approximated by a Poisson distribution with a standard deviation of 1 6 hours The facility opens from 8 am until 8 pm 12 hours daily 1 point Find the probability that no patient arrived within a 45 minute break period b 1 point The pharmacy does not want the store to be crowded Determine the probability that at least 2 patients arrived within any 15 minute duration

3 3 points A company is conducting staff development training remotely for its 65 management staff across the nation During specialty sections participants were assigned to three breakout rooms according to their specialty 17 in room 1 21 in room 2 and the rest to room 3 They are required to take a test based on their specialty a 1 5 points If a total of 8 participants failed the specialty test determine the probability that a quarter of them was in room 3 b 1 5 points Three participants were kicked out of the training by internet disruption find the probability that at least one of them is not in room 1

200nsip2 bailgga brs ankesnigna to 2 2 points The management of a particular gas station estimated that a quarter of customers do not fill their tanks It is assumed that the decision of a customer does not influence another customer 1 point On a particular day when 150 customers bought gas at the gas station how many will the management expect not to fill their tanks 1 point Among the 6 customers within a given time of the day find the probability that at least someone filled the tank

Suppose z follows the standard normal distribution Calculate the following probabilities using the ALEKS calculator Round your responses to at least three decimal places a P Z 0 84 0 b P Z 1 72 0 c P 0 91 Z 2 19 X

During the busy season it is important for the shipping manager at ShipMundo to be able to estimate the time it takes the loading crew to load a truck The shipping manager has found that she can model the load times using a normal distribution with a mean of 153 minutes and a standard deviation of 10 minutes Use this table or the ALEKS calculator to find the percentage of load times between 165 minutes and 177 minutes according to the model For your intermediate computations use four or more decimal places Give your final answer to two decimal places for example 98 23

Ravi a highway safety inspector is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway As part of an accident simulator Ravi models the boulders weights using a normal distribution with a mean of 562 kg and a standard deviation of 100 kg Use this table or the ALEKS calculator to find the percentage of boulders that weigh between 406 kg and 530 kg according to the model For your intermediate computations use four or more decimal places Give your final answer to two decimal places for example 98 23

and 0 1 Y a random variable with values iii 0 1 2 Initially we have the following partial information about their joint probability mass function Subsequently we learn the following i Given X 1 Y is uniformly distributed ii 2 3 PX Y 0 0 E Y X 0 4 5

2 The Triple E Lumber store found that 3 out of every 10 hammer drills they recently received were not properly assembled If they received 495 hammer drills about how many hammer drills can they expect to be faulty O 165 5 hammer drills

uppose Victor is conducting a study to discover a potential association between overall happiness and income level Victor andomly surveys 241 American adults and asks them to report their overall happiness and current income level Both income nd happiness were reported as low medium or high The table and summary output show the results of Victor s survey Low income Medium income High income All Pearson Observed count Expected count Chi square Observed count Expected count Chi square Observed count Expected count Chi square Observed count Chi square 31 852147 Low happiness 31 18 90 7 738849 22 22 57 0 014526 15 26 52 5 006082 68 DF 4 Medium happiness 24 26 13 0 174063 39 31 20 1 948133 31 36 66 0 874969 94 P value 0 0001 High happiness 12 21 96 4 519240 19 26 22 1 990047 48 30 81 9 586238 79 E All 67 80 94 241 3 If you wish you may download the data in your preferred format CrunchIt CSV Excel JMP Mac Text Minitab10 14 Minitab18 PC Text R SPSS TI Calc Based on Victor s table of income versus happiness which three cells have the largest contribution to the chi square test statistic Relatively small and relatively large values indicate observed counts that are smaller and larger than the expected counts respectively

Many birds are injured or killed by flying into windows It appears that birds do not see windows Can tilting windows down so that they reflect earth rather than sky reduce bird strikes Researchers placed six windows at the edge of a woods two vertical two tilted downward 20 degrees and two tilted downward 40 degrees During the next four months there were 53 bird strikes 31 on the vertical windows 14 on the 20 degree windows and eight on the 40 degree windows Does the tilt have an effect Identify the variable and select the correct explanation of why it is categorical How many levels does this variable have The variable is window orientation of bird strikes Window orientation is categorical because it takes on values that are labels for the degree of tilt It has three levels The variable is the degree of cloudiness in the sky which is categorical because it takes on values for different levels of cloudiness It has three levels clear partially cloudy and cloudy The variable is number of bird strikes which is organized by the degree of the strike It has three levels The variable is window orientation of bird strikes Window orientation is categorical because it takes on values that are labels for the degree of tilt It has six levels Select the null and alternative hypotheses that are appropriate for the study s objective P40 1 Ha all three are equally likely P40 H not all three are equally likely Ho Po P20 Ho Po P20 Ho Po P20 Ha P40 0 Ho Po P20 P40 Ha not all three are equally likely

randomly selected n 259 adults who used a desktop or laptop outside of the workplace tablets and smartphones were excluded The subjects were asked to identify the operating system of the desktop or laptop they used the most The operating systems were classified as Windows Mac OS and Linux There were no other operating systems reported in the survey The subjects were administered a test for creative imagery ability TCIA and based on the results were classified as being exceptionally artistic or not Exceptionally artistic was defined as being above the third quartile the top 25 percent of all people who took the TCIA The table contains the results of the study Exceptional Not exceptional Total Windows 46 182 228 Mac OS 4 14 18 Linux 3 10 13 Total 53 206 259 If you wish you may download the data in your preferred format Crunchlt CSV Excel JMP Mac Text Minitab14 18 Minitab18 PC Text R SPSS TI Calc The research company plans to conduct a chi square test for independence to determe if artistic ability and operating system preference are dependent Their null hypothesis is that they are independent Assuming that artistic ability and operating system preference are independent compute the expected number E of subjects who would prefer the Windows operating system and are rated as exceptional in terms of artistic ability Give your answer precise to two decimal places

Rice is one of the most widely consumed grain worldwide As increasing global temperatures hamper rice production scientists are searching for varieties exhibiting some degree of heat resistance The HT54 variety of the indica rice Oryza sativa was found to tolerate several days of high temperatures up to 48 C 118 F during its growth Researchers performed a genetic crossing experiment between the heat resistant HT54 variety and a control variety HT13 without heat resistance All seedlings in the first generation survived a heat challenge of 48 C However only 548 of the 744 plants in the second generation survived the heat challenge This suggests that heat resistance is carried by a single gene with a dominant allele and a recessive allele in which case the rice phenotype marked by heat resistance should theoretically occur in 75 of the seedlings Calculate the chi square statistic for this scenario Enter your answer rounded to three decimal places

acmillan Learning Suppose Sora is arguing with her mother Jane Jane believes that Sora eats mostly candy and doesn t eat enough fruits and vegetables but Sora claims that she eats candy fruits and vegetables equally often To test Sora s claim Jane carefully monitors Sora s eating habits for several weeks She records the number of times that Sora eats fruits vegetables and candy Jane conducts a chi square test for goodness of fit to test Sora s claim Jane s results are summarized in the table Type of food Observed Fruits 53 k Vegetables Candy 61 86 P Test proportion 0 333 0 333 0 333 Expected 66 667 66 667 66 667 Contribution to chi square 2 802 0 482 5 606 Chi square statistic 8 8900 Degrees of freedom 2 What is the P value for Jane s chi square test for goodness of fit Round your answer to three decimal places Based on Jane s results and assuming a significance level of a 0 05 what should Jane conclude about Sora s claim that she eats all three types of food equally often Because P a there is insufficient evidence against Sora s claim Because P a there is significant evidence against Sora s claim Because P a there is insufficient evidence against Sora s claim Because P a there is significant evidence against Sora s claim

Consider the value of such that 0 05 of the area under the curve is to the right of 7 Step 1 of 2 Select the graph which best represents the given description of Answer 0 0 t t t 0 0 Tables

A survey of 1010 college seniors working towards an undergraduate degree was conducted Each student was asked Are you planning or not planning to pursue a graduate degree Of the 1010 surveyed 658 stated that they were planning to pursue a graduate degree Construct and interpret a 98 confidence interval for the proportion of college seniors who are planning to pursue a graduate degree Round to three decimal places M Lower Duuniu 0 021 upper uur v 0 ve are are planning to pursue a graduate degree is between 0 621 and 0 680 at the proportion of college seniors wITU OB Lower bound 0 616 Upper bound 0 686 We are 98 confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0 616 and 0 686 OC Lower bound 0 612 Upper bound 0 690 We are 98 confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0 612 and 0 690 O D Lower bound 0 620 Upper bound 0 682 We are 98 confident that the proportion of college seniors who

f Now assume instead the government increases spending without changing taxes to close the recessionary gap What effect will this policy have on the national debt

A university dean is interested in determining the proportion of students who receive some sort of financial aid Rather than examine the records for all students the dean randomly selects 200 students and finds that 118 of them are receiving financial aid If the dean wanted to estimate the proportion of all students receiving financial aid to within 4 with 90 reliability how many students would need to be sampled Round up to the nearest whole number OA 99 B 410 C 249 17

Five randomly selected men were asked to run on a treadmill for 6 minutes After the 6 minutes their pulses were measured and the following data were obtained 122 114 97 101 90 Construct a 95 Z interval or a 95 t interval about the population mean Assume the data come from a population that is approximately normal with no outliers Round the lower and upper bounds to one decimal place CLEE OA Lower bound 92 4 Upper bound 117 2 We are 95 confident that the mean pulse rate of men after 6 minutes of exercise is between 92 4 and 117 2 beats per minute O B Lower bound 86 8 Upper bound 122 8 The mean pulse rate for 95 of all men after 6 minutes of exercise is between 86 8 and 122 8 beats per minute OC Lower bound 93 4 Upper bound 116 2 We are 95 confident that the mean pulse rate of men after 6 minutes of exercise is between 93 4 and 116 2 beats per minute O D Lower bound 88 7 Upper bound 120 9 We are 95 confident that the mean pulse rate of men after 6 minutes of exercise is between 88 7 and 120 9 beats per minute

In a random sample of 60 dog owners enrolled in obedience training it was determined that the mean amount of money spent per owner was 109 33 per class and the standard deviation of the amount spent per owner was 12 Construct and interpret a 95 confidence interval for the mean amount spent per owner for an obedience class Round to the nearest cent O A Lower bound 106 23 Upper bound 112 43 We are 95 confident that the mean amount spent per dog owner for a single obedience class is between 106 23 and 112 43 B Lower bound 106 29 Upper bound 112 37 We are 95 confident that the mean amount spent per dog owner for a single obedience class is between 106 29 and 112 37 OC Lower bound 106 78 Upper bound 111 88 We are 95 confident that the mean amount spent per dog owner for a single obedience class is between 106 78 and 111 88 OD Lower bound 106 74 Upper bound 111 92 We are 95 confident that the mean amount spent per doa

A pollster wishes to estimate the number of left handed scientists What size sample should be obtained in order to be 98 confident that the sample proportion will not differ from the true proportion by more than 4 A previous study indicates that the proportion of left handed scientists is 12 Round up to the nearest whole number OA 358 B 15 OC 254 OD 406

A local bank needs information concerning the savings account balances of its customers A random sample of 15 accounts was checked The mean balance was 686 75 with a standard deviation of 256 20 Find a 98 confidence interval for the true mean Assume that the account balances are normally distributed Round to the nearest cent OA 326 21 437 90 OB 487 31 563 80 OC 238 23 326 41 D S513 17 860 33

Find the critical t value that corresponds to 99 confidence and n 10 Round to three decimal places A 2 821 B 2 262 O C 3 250 D 1 833

g Draw a correctly labeled graph of the loanable funds market and show the effect of the change in the national debt on the equilibrium real interest rate

A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation What size sample should be obtained in order to be 98 confident that the sample proportion will not differ from the true proportion by more than 3 Round up to the nearest whole number OA 20 O B 1 068 C 3 017 1 509 On

A group of 19 randomly selected employees has a mean age of 22 4 years with a standard deviation of 3 8 years Construct a 99 confidence interval for the population mean Assume the population has a normal distribution Round to one decimal place OA 19 9 24 9 OB 17 2 23 6 OC 16 3 26 9 OD 18 7 24 1

A random sample of 10 parking meters in a resort community showed the following incomes for a day Assume the incomes are normally distributed Find the 95 confidence interval for the true mean Round to the nearest cent 3 60 4 50 2 80 6 30 2 60 5 20 6 75 4 25 8 00 3 00 OA 4 81 6 31 OB 2 11 5 34 OC 3 39 6 01 D 1 35 2 85

Determine the critical value Za 2 that corresponds to the given level of confidence rounding to two decimal places 88 A 1 56 OB 1 18 O C 1 21 D 0 81

A sample of 15 randomly selected math majors has a grade point average of 2 86 with a standard deviation of 0 78 Construct a 90 confidence interval for the population mean Assume the population has a normal distribution Round to two decimal places OA 2 28 3 66 OB 2 51 3 21 OC 2 41 3 42 D 2 37 3 56

A survey of 2 620 musicians showed that 339 of them are left handed Find a point estimate for p the population proportion of musicians that are left handed rounding to three decimal places O A 0 115 B 0 871 O C 0 149 OD 0 129

A survey of 500 non fatal accidents showed that 113 involved faulty equipment Find a point estimate for p the population proportion of accidents that involved faulty equipment rounding to three decimal places O A 0 292 B 0 184 OC 0 774 D 0 226

An economy is currently in a recession a Draw a single correctly labeled graph with both the short run and long run Phillips curves Label the current short run equilibrium as point X

A normal distribution has a mean of 37 and a standard deviation of 3 Find the probability that a randomly selected x value from the distribution is in the given interval 25 28 31 34 37 0 68268 25 28 31 X 34 X 37 X 40 43 46 40 43 46 49 Q 49 a

Woodland and Willow Road are schools in different states The heights of students at Woodland have a population mean of 54 5 inches and a standard deviation of 1 7 inches The heights of students at Willow Road have a population mean of 61 2 inches with a standard deviation of 2 1 inches For each school the distribution of the heights of students is clearly bell shaped Alan is a student at Woodland and is 50 inches tall Tony is a student at Willow Road and is 54 inches tall a Find the z scores of Alan s height as a student at Woodland and Tony s height as a student at Willow Road Round your answers to two decimal places z score of Alan s height z score of Tony s height X b Relative to his population which student is taller Choose the best answer based on the z scores of the two heights O Alan Tony X G 3

Center to see if she really has psychic abilities While talking to her on the phone we ll thoroughly shuffle a standard deck of 52 cards which is made up of 13 hearts 13 spades 13 diamonds and 13 clubs and draw one card at random We ll ask Clara to name the suit heart spade diamond or club of the card we drew After getting her guess we ll return the card to the deck thoroughly shuffle the deck draw another card and get her guess for the suit of this second card We ll repeat this process until we ve drawn a total of 14 cards and gotten her suit guesses for each Assume that Clara is not clairvoyant that is assume that she randomly guesses on each card Answer the following If necessary consult a list of formulas a Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution that is the expectation of the relevant random variable Do not round your response 0 b Quantify the uncertainty of your estimate by giving the standard deviation of the distribution Round your response to at least three decimal places

Circles G and H have centers 0 3 and 4 5 and radii of lengths 2 and 10 respectively To prov circle G similar to circle H each of the follow transformations must be performed except O dilate circle G by a scale factor of O dilate circle G by a scale factor of 5 O translate circle G 8 units down Otranslate circle G 4 units left

There is a weekend fishing competition that Ivan participates in each year There are several other fishing boats that participate in this competition Ivan caught 42 fish at the competition this year Among all the competitors the number of fish caught this year had a mean of 43 fish and a standard deviation of 9 fish Find the Z score of the number of fish that Ivan caught relative to the numbers of fish caught by all the competitors Round your answer to two decimal places 0 Z X

14 A study examined the effect of protein consumption on weight gain in rats Investigators obtained 14 female rats and randomly assigned 7 of them to a low protein diet and the other 7 to a high protein diet After 60 days the weight gained by each rat was recorded in grams Here are the summary findings displayed as mean standard deviation Low Protein Diet 101 3 20 6 Researchers want to know if the amount of protein in the rats diet significantly affects their weight gain What are the corresponding null and alternative hypotheses a Ho HHigh Low Vs H HHigh Low b Vs H HHigh Low H Low C Ho HHigh Vs H High d Ho High Low H High 127 5 and Low 101 3 Ho High Low 127 5 and Low 101 3 Vs High Protein Diet 127 5 21 1 15 Based on the data software gives the T statistic 2 35 with df 12 Researchers want to know if the amount of protein in the rats diet significantly affects their weight gain What should they conclude at significance level 5 a Reject the alternative hypothesis b Fail to reject the alternative hypothesis c Reject the null hypothesis d Fail to reject the null hypothesis

10 A manufacturer claims that the mean driving cost per mile M of its vehicles is less than that of its leading competitor You conduct a study using 30 randomly selected vehicles from the manufacturer and 32 from the leading competitor Here are some summary statistics from the study Sex Null Mean 0 48 mi 0 51 mi Manufacturer Competitor State the null and alternative hypotheses in terms of HM Hc Conclusion Standard deviation Alternative 11 What is your conclusion based on the R output below xbar 0 48 sx 0 05 nx 30 ybar 0 51 sy 0 07 ny 32 data 0 05 mi 0 07 mi t 1 9509 df 56 147 p value 0 02803 c Reject the null hypothesis d Fail to reject the null hypothesis 12 For problem 10 what can we conclude at significance level 5 a Reject the alternative hypothesis b Fail to reject the alternative hypothesis

17 Which of the following statements would lead us to believe that the t procedures were NOT safe to use here The experiment was not double blinded The distributions of the data were skewed or had outliers b c The population standard deviations were not known d The t procedures are always safe to use in a randomized experiment

7 Researchers examined the effect of phosphate supplementation on bone formation in 6 healthy adult dogs For each dog bone formation was measured twice once after 12 weeks of phosphate supplementation and once after a 12 week control period The results in percent bone growth per year are shown below Do these data provide evidence that phosphate supplementation significantly stimulates bone formation Dog ID Control Phosphate Difference 1 1 73 8 16 6 43 2 3 4 5 3 37 3 59 2 05 1 86 4 58 3 98 5 24 3 04 1 21 0 39 3 19 1 18 6 3 60 7 03 3 43 What are the appropriate null and alternative hypotheses Vs H HControl Phosphate a Ho HControl Phosphate b Ho HDifference Control Phosphate 0 Vs H Difference Control Phosphate Ho HControl Phosphate Vs H HControl C Phosphate Avg 2 7 5 34 2 64 0 S D 0 908 1 925 2 215

13 Under which of the following conditions can a large P value arise a Ho is indeed true b Ho is not actually true but too close to the real population distribution for us to tell them apart statistically c Ho is definitely not true but the sample size is too small or the variability is too great to reach significance d All of the above

5 Based on this test and using a significance level of 0 05 what should we conclude a Reject the null hypothesis P 0 05 b Reject the null hypothesis P 0 05 c Fail to reject the null hypothesis P 0 05 d Fail to reject the null hypothesis P 0 05

3 Here are some summary statis university

1D Practice 1 Researchers in an early childh vocabularies of young children Age Mean

7 The histogram represents the distribution of the number of seconds it took for each of 50 students to find the answer to a trivia question using the internet Which interval contains the median 24 22 20 18 16 14 12 086420 10 0

1 Twenty students participated in a psychology experiment w rates in two different situations 70 70 75 75 80 80 85 90 situation A 85 90 situation B 95 00 95 a What are the appropriate measures of center and varia data Explain your reasoning

2 Which of the dot plots shows a skewed distribution C A B 1 1 9 0 5 1 10 1 2 1 3 11 12 1 4 1 5 2 2 5 3 13 1 5 3 5 1 6 14 15 4 4 5 1

6 The dot plots display the height rounded two different tree farms 3 3 4 4 5 LO 5 6 6 00 7 7 8 heig 000 8

A national chain of department stores ranks its 900 000 salespeople by the monetary value of their sales Ahmad s sales are at the 93rd percentile Teresa s sales are at the 44th percentile If necessary consult a list of formulas a Which of the following must be true about Ahmad s sales About 93 of the salespeople had sales lower in value than Ahmad The value of Ahmad s sales were about 93 of the chain s total O The value of Ahmad s sales was in the bottom half of all of the salespeople O Ahmad sold 9300 in merchandise b Which of the following must be true about Ahmad s and Teresa s sales Both Ahmad and Teresa had sales higher in value than the median Both Ahmad and Teresa had sales lower in value than the median O Ahmad s sales were higher in value than Teresa s sales O Teresa s sales were higher in value than Ahmad s sales X

4 Here are two box plots 95 95 100 100 box