Statistics Questions

Complete the process of solving the equation Fill in the missing term on each line Simplify any fractions 3y 1 1 3y y Subtract 1 from both sides Divide both sides by 3

Find the y intercept of the line y 8 13 Write your answer as an integer or as a simplified proper or improper fraction not as an ordered pair

Give the mode for following GFDT Recall there is a definition for the mode appropriate for GFDTS Data Frequency 50 54 10 55 59 19 60 64 10 65 69 9 70 74 5 75 79 4 80 84 4 85 89 1 90 94 1

Here is a sample data set 533 1 619 9 541 2 526 6 434 6 526 6 478 6 539 3 534 4 505 5 431 2 613 4 471 5 541 3 444 6 533 7 468 8 451 9 405 7 538 3 528 9 451 1 549 3 418 2 468 8 518 1 495 8 544 1 468 539 3 631 485 5 483 5 468 8 536 8 472 1 539 1 539 3 608 8 617 7 492 9 509 8 458 1 536 3 531 3 405 4 606 6 526 7 534 2 626 8 440 3 459 6 617 8 500 6 Find the first quartile for this data set Q Find the third quartile for this data set Q3 Find the interquartile range for this data set IQR

Outside a home there is an 8 key keypad with letters A B C D E F G and H that can be used to open the garage if the correct eight letter code is entered Each key may be used only once How many codes are possible The number of possible codes is

Determine whether the statement below is true or false If it is false rewrite it as a true statement When you divide the number of permutations of 11 objects taken 3 at a time by 3 you will get the number of combinations of 11 objects taken 3 at a time Choose the correct answer below O A The statement is false A true statement is When you divide the number of combinations of 11 objects taken 3 at a time by 3 you will get the number of permutations of 11 objects taken 3 at a time OB The statement is false A true statement is When you multiply the number of permutations of 11 objects taken 3 at a time by 3 you will get the number of combinations of 11 objects taken 3 at a time OC The statement is false A true statement is When you divide the number of permutations of 11 objects taken 3 at a time by 11 3 you will get the number of combinations of 11 objects taken 3 at a time D The statement is true

The percent distribution of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old is shown in the pie chart Find each probability a Randomly selecting a mother 30 39 years old P 30 to 39 b Randomly selecting a mother not 30 39 years old P not 30 to 39 Round to the nearest thousandth as needed c Randomly selecting a mother less than 45 years old P less than 45 Round to the nearest thousandth as needed d Randomly selecting a mother at least 20 years old P at least 20 Round to the nearest thousandth as needed Round to the nearest thousandth as needed SOCCE Number of Multiple Births 00 15 19 1 6 20 24 6 3 25 29 21 3 30 34 37 3 35 39 24 6 40 44 5 3 45 54 3 6

Approximate the measures of center for following GFDT Data Frequency 70 74 75 79 80 84 85 89 90 94 95 99 100 104 105 109 110 114 mode median mean Report mode and 2 4 7 13 18 10 11 0 4

The 81 th percentile of lightbulb lifespan is 1500 hours What does this mean of light bulbs have a lifespan of less than or equal to 1500 hours 06 CH

Calculate the 10th percentile of the data shown X 1 1 9 11 3 12 2 13 5 15 5 21 2 23 3 27 9

Here is a data set 12 21 21 43 10 18 37 23 36 35 39 12 23 42 27 18 31 17 22 28 16 20 49 26 23 10 22 26 26 26 You are examining 1 00226788 2 01122333666678 3 15679 the data with a stem and leaf plot Here is the start of the plot Finish the

The highway mileage mpg for a sample of 8 different models of a car company can be found below Find the 5 number summary and use it to create a boxplot 18 21 23 26 29 32 35 35 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 mpg Q 4 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 mpg Q t H O 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 mpg a t O 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 mpg 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 mpg

A set of data items is normally distributed with a mean of 112 and a standard deviation of 15 Convert each of the following data items to a z score Round your answer to the nearest hundredth a 212 Z b 94 Z

Calculate the standard deviation of the sample data shown to X 21 8 12 4 25 1 19 6 16 3 8 7 26 8

Approximate the mean for following GFDT Data Frequency 40 44 1 45 49 1 50 54 4 55 59 7 60 64 8 65 69 10 70 74 11 75 79 21 80 84 12 mean

A standard deck of cards contains 52 cards One card is selected from the deck a Compute the probability of randomly selecting a club or diamond b Compute the probability of randomly selecting a club or diamond or heart c Compute the probability of randomly selecting a king or club a P club or diamond Round to three decimal places as needed b P club or diamond or heart Round to three decimal places as needed c P king or club Round to three decimal places as needed

The table below shows the scores of a group of students on a 10 point quiz Test Score 3 st 4 5 56 7 8 9 10 Frequency 24 1 3 3 2 1 4 The mean score on this test is The median score on this test is

A survey of a group s web habits for the past month obtained the following information 46 visited Facebook 47 visited LinkedIn 35 visited Google 29 visited Facebook and LinkedIn 19 visited Facebook and Google 23 visited LinkedIn and Google 14 visited all three sites Find the percentage that visited none of these three sites last month

4 different color dice are rolled and the numbers showing are recorded How many different outcomes are possible Your answer is

The Venn diagram here shows the cardinality of each set Use this to find the probability of observing the given set A 5 C 6 7 2 14 8 9 B 4

A jar contains 5 red marbles numbered 1 to 5 and 10 blue marbles numbered 1 to 10 A marble is drawn at random from the jar Find the probability that the marble is red or odd numbered

In how many different ways can a police department arrange a lineup if each lineup contains 8 people

In this question we will formulate a measure to quantify the level of association between the two categorical variables Such a measure is often used in a statistical test called Chi square test for assessing whether there is an association between two categorical variables This question is also used to motivate the learning of independence and to connect the concept back to what we have learnt in the course Let s revisit the example we have looked at in the course How is diet type high cholesterol diet versus low cholesterol diet related to the risk of coronary heart disease Data of 23 individuals High cholesterol diet Low cholesterol diet From the table we find that the probability of having heart disease is 13 23 and the probability of having high cholesterol diet is 15 23 Similarly we can find the probability of not having heart disease and the probability of having low cholesterol diet Heart disease No heart disease Total i 11 iii 4 15 ii 2 iv 6 8 13 10 23 Part a If there is no association between the two variables i e the two are independent the probability of having heart disease and high cholesterol diet is Round to four decimal places 0 4783 Part b If the two variables are independent we should expect the number of individuals with heart disease and high cholestoral diet to be the probability in Part a multiplied by 23 individuals which is Round to two decimal places 0 37 Part c Repeating Part b we find that the expected number of individuals for the cells ii iii iv respectively on the table are 4 52 6 52 3 48 The following measure called Chi square test statistic x Observed Expected Expected

According to a recent census 18 of the people in the United States are of Hispanic origin One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole She looks at their most recent survey data which was a random sample of 442 county residents and found that 41 of those surveyed are of Hispanic origin Complete parts a through d below b Name the model and check appropriate conditions for a hypothesis test What kind of test is this Two proportion t test One proportion z test Difference in differences test O Proportional t test Check the appropriate conditions for a hypothesis test Select the correct choice below and fill in the answer boxes within your choice Round to one decimal place as needed OA The 442 residents were a random sample from the county of interest The standard deviation of p is less than 0 5 One expects npo successes and ngo failures which are both more than 20 OB The 442 residents were a random sample from the county of interest The sample size is more than 100 One expects npo successes and failures which are both more than 10 nao OC The 442 residents were a random sample from the county of interest 442 is likely less than 10 of the population of a county

Someone hands you a box of 17 chocolate covered candies telling you that 8 are vanilla creams and the rest are peanut butter You pick candies at random and discover the first 3 you eat are all vanilla Consider a result to be surprising if there is less than a 5 chance of observing it given your expectations Complete parts a through c below a If there really were 8 vanilla and 9 peanut butter candies in the box what is the probability that you would have picked 3 vanillas in a row Round to three decimal places as needed

Some people are concerned that new tougher standards and high stakes tests adopte many states have driven up the high school dropout rate The National Center for Education Statistics reported that the high school dropout rate for the year 2012 was 7 0 One school district whose dropout rate has always been very close to the nation average reports that 134 of their 1789 high school students dropped out last year Is thi evidence that their dropout rate may be increasing Explain Determine the hypotheses for this test Ho P 0 07 HA P 0 07 Type integers or decimals Do not round Compute the test statistic 0 81 Round to two decimal places as needed Find the P value 0 Round to three decimal places as needed

In a survey of 275 professional athletes it was found that 126 of them owned a convertible 124 of them owned a giant screen TV and 123 owned a sporting goods store 18 owned a convertible and a store 45 owned a TV and a store and 69 owned a covertible and a TV 11 owned all three items 1 How many athletes did not own any of the three items 2 How many owned a covertible and a TV but not a store 3 How many athletes owned a convertible or a TV 4 How many athletes owned exactly one type of item in the survey 5 How many athletes owned at least one type of item in the survey 6 How many owned a TV or a store but not a convertible

For this question you will use A 316 The solution A is a constant function B is concave up and approaches the value of 651 C decreases and approaches z D increases and approaches a horizontal asymptote A

The probability statement that a student does not complete the exam in 130 minutes was determined to be P x 130 The corresponding probability statement for the normal random variable z is P Z 1 50 Recall that the normal probability table below gives the area under the curve to the left of a given z value and the entire area under this curve is 1 Here we want the area to the right of z 1 50 so we can subtract the area to the left of z 1 50 from 1 Z 0 00 0 01 0 02 0 03 1 4 0 9192 0 9207 0 9222 0 9236 1 5 0 9332 0 9345 0 9357 0 9370 0 9452 0 9463 0 9474 0 9484 0 9495 0 9505 0 9515 0 9525 0 9535 0 9545 0 04 0 05 0 9251 0 9265 0 9382 0 9394 0 06 0 07 0 08 0 9279 0 9292 0 9306 0 9406 0 9418 0 9429 0 09 0 9319 0 9441 1 6 Use the table excerpt above to find the probability that a student takes longer than 130 minutes to complete the exam rounding to four decimal places P Z 1 50 1 0 0495 X 0 0974 X

in a survey of 275 professional athletes it was found that 126 of them owned a convertible 124 of them owned a giant screen TV and 123 owned a sporting goods store 18 owned a convertible and a store 45 owned a TV and a store and 69 owned a covertible and a TV 11 owned all three items 1 How many athletes did not own any of the three items 2 How many owned a covertible and a TV but not a store 3 How many athletes owned a convertible or a TV 4 How many athletes owned exactly one type of item in the survey 5 How many athletes owned at least one type of item in the survey 6 How many owned a TV or a store but not a convertible

1 point Ten randomly selected people took an IQ test A and next day they took a very similar IQ test B Their scores are shown in the table below Person ABCDEFGHI J Test A 87 73 101 122 99 90 111 96 107 119 Test B 88 72 102 124 98 91 108 95 106 120 You should be able to copy and paste the data into Sheets or Excel If it doesn t copy correctly then try the special paste options 1 Consider Test A Test B Use a 0 05 significance level to test the claim that people do better on the second test than they do on the first Note You may wish to use software a What test method should be used OA Two Sample z test OB Two Sample t test OC Matched Pairs t test A b The test statistic is c Is there sufficient evidence to support the claim that people do better on the second test SOA No OB Yes 2 Construct a 95 confidence interval for the mean of the differences Again use Test A Test B F

a Provide a 90 confidence interval for the population mean Recall that a confidence interval is calculated using the sample mean and a margin of error The margin of error will vary depending on the level of confidence a the population standard deviation o and the size of the sample n This value will be added to and subtracted from the sample mean x using the following formula where Za 2 is the value of z that gives an area of z a in the upper tail of the standard normal probability distribution 2 6 V n below x a 2 The value of a is found by setting the confidence level equal to 1 a and solving for a Here we have 1 a 0 90 so a 0 10 and 2 Confidence Level a 90 95 99 O NA a 2 za 2 0 10 0 05 1 645 0 05 0 025 1 960 0 01 0 005 2 576 For a 90 confidence level the necessary value for z a 2 N is Common values for z 2 are given

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories Smooth Rhythm Standard The results were then presented to the owner in the following Venn Diagram Smooth 5 12 15 Standard 6 Rhythm 7 14 a Q If a student is chosen at random what is the probability that Write your answers in percent form Round to the nearest tenth of a percent a The student has competed in none of the categories b The student has competed in all three of these categories c The student has competed in Smooth or Standard but not Rhythm d The student has competed in Rhythm and Standard but not Smooth e The student has competed in Rhythm

Here is a sample data set 484 446 8 390 8 539 5 463 4 424 5 447 5 420 4 518 7 368 2 410 9 347 1 457 5 485 4 485 4 589 4 464 4 554 6 512 5 463 5 303 4 482 2 386 6 423 2 429 5 420 4 485 4 407 3 498 2 444 6 398 3 456 451 1 530 7 442 7 453 6 481 6 484 5 420 4 453 6 547 1 475 1 390 2 411 7 541 9 Find the first quartile for this data set Q Find the third quartile for this data set Q3 444 5 506 7 466 6 544 355 2 503 3 422 7 359 6 422 9 Find the interquartile range for this data set IQR

A girl has 8 skirts 9 blouses and 9 pairs of shoes How many different skirt blouse shoe outfits can she wear Assume that each item matches all the others so she is willing to wear any combination Your answer is

In the 6 51 lottery game a player picks six numbers from 1 to 51 How many different choices does the player have Your answer is

Suppose a designer has a palette of 6 colors to work with and wants to design a flag with 3 vertical stripes all of different colors How many possible flags can be created

A pianist plans to play 3 pieces at a recital In how many ways can she arrange these pieces in the program Your answer is

In how many ways can 3 students from a class of 15 be chosen for a field trip Your answer is

How many ways can 8 candles be arranged on a shelf

You may need to use the appropriate appendix table or technology to answer this question A random sample of 81 credit sales in a department store showed an average sale of 65 00 From past data it is known that the standard deviation of the population is 26 a Determine the standard error of the mean in dollars Round your answer to the nearest cent b With a 0 95 probability what can be said about the size of the margin of error There is a 0 95 probability that the distance between the sample mean and the population mean will equal the margin of error O There is a 0 95 probability that the distance between the sample mean and the population mean will be greater than or equal to the margin of error O There is a 0 95 probability that the margin of error and the population mean are equal O There is a 0 95 probability that the sample mean and the population mean are equal O There is a 0 95 probability that the distance between the sample mean and the population mean will be less than or equal to the margin of error c What is the 95 confidence interval of the population mean in dollars Round your answers to the nearest cent to

Let P U 0 28 and P V 0 28 and P V 0 47 Events U and V are mutually exclusive Find P U or V O 1 6785714285714 O 0 59574468085106 O 0 75 O 0 1316 O 0 19 O 0 19

With a population of 3500 people we randomly sample 139 people without replacement Is it reasonable to assume that the trials are sampled independently O No because the sample size is greater than or equal to 5 of the population size O No because the sample size is less than 5 of the population size O Yes because the sample size is less than 5 of the population size OYes because the sample size is greater than or equal to 5 of the population rito

The z value corresponding to a 0 80 cumulative probability was found to be 0 84 Thus the necessary return x will be 0 84 standard deviations above the mean return Recall the formula to convert a given value x to the standard normal random z Z X x 0 Here we have the values of z and o but need to find x Solve the equation for x X 1 4 7712 On Fu Sy Rel Sets

76 The attention span of a two year old is exponentially distributed with a mean of about eight minutes Suppose we randomly survey 60 two year olds a In words X b X c In words X d X e Before doing any calculations which do you think will be higher Explain why i The probability that an individual attention span is less than 10 minutes ii The probability that the average attention span for the 60 children is less than 10 minutes f Calculate the probabilities in part e g Explain why the distribution for X is not exponential

creating a test for the Zika virus The incidence of a Zika is low 5 percent in the general population There is a trial version but it sometimes misses the disease The probability of a false negative is 13 percent Similarly someone who does not have Zika will sometimes get a positive reading The probability of this is 20 percent Fill in the tree diagram and Answer in percent to 2 decimal places Marginal Probabilities P D P no D Conditional Probabilities P positive D P negative D P positive no D False negative False Positive Joint Probabilities 11 P D and positive P D and negative P no D and positive P no D and negative P negative no D Calculate the probability that a positive test result means someone has Zika

2 percent of a certain company s life insurance policy holders are smokers For each nonsmoker the probability of dying during the year is 0 015 For each smoker the probability of dying during the year is 0 05 Round your answers to at least 4 decimal places a Find the probability that a randomly selected policyholder died last year b Find the probability that a randomly selected policy holder who died last year was a smoker

90 The average length of a maternity stay in a U S hospital is said to be 2 4 days with a standard deviation of 0 9 days We randomly survey 80 women who recently bore children in a U S hospital a In words X b In words X c X d In words EX e EX f Is it likely that an individual stayed more than five days in the hospital Why or why not g Is it likely that the average stay for the 80 women was more than five days Why or why not h Which is more likely I An individual stayed more than five days ii The average stay of 80 women was more than five days i If we were to sum up the women s stays is it likely that collectively they spent more than a year in the hospital Why or why not

than percents In a family with 5 children what is the probability of having 3 boys and then 2 girls in that order Exclude multiple births and assume all outcomes are equally likely In a family with 5 children what is the probability of having 3 boys and 2 girls in any order Exclude multiple births and assume all outcomes are equally likely

75 Salaries for entry level managers at a restaurant chain are normally distributed with a mean of 44 000 and a standard deviation of 6 500 We randomly survey 10 managers from these restaurants a In words X b X c In words EX d EX e Find the probability that the managers earn a total of over 400 000 f Find the 90th percentile for an individual manager s salary g Find the 90th percentile for the sum of ten managers salary h If we surveyed 70 managers instead of ten graphically how would that change the distribution in part d i If each of the 70 managers received a 3 000 raise graphically how would that change the distribution in part b