Statistics Questions

The National Academy of Science reported that 33 of research in mathematics is published by US authors The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33 He has no indication of whether the percentage has increased or decreased since that time He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors Does this evidence support the mathematics chairperson s claim that the percentage is no longer 33 Use a 0 01 level of significance Step 1 of 3 State the null and alternative hypotheses for the test Fill in the blank below Ho p 0 33 Ha P 0 33

13 A new surgical procedure is said to be successful 80 of the time Suppose the operation is performed five times and the results are assumed to be independent of one another 12 points A List the values A may take on B p q n C What is the probability that all 5 operations are successful D What is the probability exactly 4 are successful E What is the probability that less than 2 are successful A F If less than 2 operations were successful how would you feel about the performance of the surgical team Explain

10 Suppose that the probability that an adult in America will watch the upcoming World Series is 40 Each person is considered independent We are interested in the number of adults in America we must survey until we find one who will watch the World Series 10 points A This is a B List the values that X may take on C How many adults in America do you expect to survey until you find one who will watch the World Series distribution p VD Find the probability that you must ask 7 people I E Find the probability that you must ask 3 or 4 people

performance of the sur BONUS A package of 6 light bulbs contains 2 defective bulbs If 3 bulbs are selected for use find the probability none are defective 4 points

An environmentalist wishes to conduct a hypothesis test on the percentage of cars driven in the city that are hybrids Is it sufficient for him to use a simple random sample of 152 cars if hybrids currently account for 7 of the car sales in the country and he claims that the percentage of hybrids in the city is higher than that Answer O Yes Keypa Keyboard Shortcu Tables

One study claimed that 89 of college students identify themselves as procrastinators A professor believes that the claim regarding college students is too high The professor conducts a simple random sample of 184 college students and finds that 157 of them identify themselves as procrastinators Does this evidence support the professor s claim that fewer than 89 of college students are procrastinators Use a 0 02 level of significance Step 3 of 3 Draw a conclusion and interpret the decision Answer Keypad Keyboard Shortcuts Tables We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0 02 level of significance that fewer than 89 of college students are procrastinators O We reject the null hypothesis and conclude that there is sufficient evidence at a 0 02 level of significance that fewer than 89 of college students are procrastinators We reject the null hypothesis and conclude that there is insufficient evidence at a 0 02 level of significance that fewer than 89 of college students are procrastinators We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0 02 level of significance that fewer than 89 of college students are procrastinators

One study claimed that 89 of college students identify themselves as procrastinators A professor believes that the claim regarding college students is too high The professor conducts a simple random sample of 184 college students and finds that 157 of them identify themselves as procrastinators Does this evidence support the professor s claim that fewer than 89 of college students are procrastinators Use a 0 02 level of significance Step 2 of 3 Compute the value of the test statistic Round your answer to two decimal places Answer Tables Keypad

6 Assume each outcome in the sample space represented by the Venn diagram below is equally likely Find P AB A B Round your answer to the nearest hundredths Answer Previous Answer 0 79 Return to queniqu

Question 7 of 15 7 Find the variance of the sample data set 3 4 6 5 2 Answer Previous Answer 2 5

The table shows the educational attainment of the population of a country ages 25 and over expressed in millions Find the probability that a randomly selected person aged 25 or over has completed four years of high school only or some college but less than four years Male Female Total Years of High School Less than 4 14 4 only 31 15 29 The probability is Type an integer or a simplified fraction 28 59 Years of College Some less than 4 22 20 42 4 or more 24 16 40 Total 79 170

The game of Scrabble has 100 tiles The diagram shows the number of tiles for each letter and the letter s point value One tile is drawn from Scrabble s 100 tiles Find each probability a Find the probability of selecting a V b Find the probability of not selecting a V a The probability of selecting a V is Type an integer or a simplified fraction A 9 F2 K P 2 U4Z B 2 G 3 L 4 Q V 2 C2 H2 M2 R6 W2 D 4 N 6 S X 1 O T Y 2 E 12 1 9 J 2A Paint

The table shows the educational attainment of the population of a certain country ages 25 and over expressed in millions Find the probability that a randomly selected person aged 25 or over has completed four years of high school only or is male The probability is Male Female Total Years of High School Less than 4 16 14 30 4 only 29 32 61 Type an integer or a simplified fraction Years of College Some less than 4 25 3 25 50 4 or more 19 16 35 Total 89 87 176

The table shows the distribution by age of a random sample of 2820 moviegoers ages 12 74 If one moviegoer is randomly selected from this population find the probability expressed as a simplified fraction that the moviegoer is not in the 12 24 age range The probability is Type an integer or a simplified fraction MIN Age Distribution of Moviegoers Number 1060 730 820 210 Ages 12 24 25 44 45 64 65 74

8 46 A farmer uses a lot of fertilizer to grow his crops The farmer s manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B s fertilizer does He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch respectively Assume the distribution of nitrogen in fertilizer is normally distributed Let 1 and 42 represent the average amount of nitrogen per batch for fertilizers A and B respectively Which of the following is the appropriate conclusion at the 5 significance level Multiple Choice Reject Ho we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B Reject Ho we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B Fail to reject Ho we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B Fail to reject Ho we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B

40 A logistic function was used to model the number of people who catch a certain virus V based on age measured in t years The function v t 35 1 20e 0 35 Assuming the model is accurate do more 30 year olds or 60 year olds catch the virus 1 More 60 year olds catch the virus since V 30 V 60 2 More 30 year olds catch the virus since V 30 V 60 3 More 60 year olds catch the virus since V 30 V 60 4 More 30 year olds catch the virus since V 30 V 60

The recessive alleles for cinnibar eyes cn and vestigial wings vg identify two autosomal genes on the third chromosome of Drosophila melanogaster When females heterozygous at these two genes cn cn vg vg were crossed with cinnibar eyed vestigial winged males the following classes and numbers of progeny n 1000 were obtained Wild type eye color wild type wings 42 Wild type eye color vestigial wings 464 Cinnibar eye color vestigial wings 38 Cinnibar eye color wild type wings 456 Based upon these results the map distance between the cn and vg genes is estimated to be 4 map units 8 map units 46 map units 92 map units

12 A particular school has 550 female students and 590 male students A random sample of 30 students was surveyed for suggestions about social activities for the following school year a Is it possible that the sample included only male students b Would a sample consisting entirely of male students be representative of the school population Explain your reasoning

5 A pollster wants to find out if citizens are satisfied with the city council Which procedure would be most appropriate for obtaining a statistically unbiased sample a interviewing people at a popular local shopping centre b surveying people whose names have been randomly chosen from the telephone book c placing an advertisement in the local newspaper asking for mail in responses d mailing a questionnaire to people whose names have been chosen randomly from a list of customers of the municipal utility company

4 A college president wants to find out which courses students consider to be of the most benefit to them Which procedure would be most likely to produce a statistically unbiased sample a asking students to mail in a questionnaire b surveying a random sample of students taken from the list of all students C surveying the first hundred students on an alphabetical list d having students complete a questionnaire on the college web site

3 A large corporation wants to find out which benefits plan its employees would prefer Which procedure would be most likely to obtain a statistically unbiased sample a surveying a random sample of employees from a list of all employees b inviting all employees to indicate their choices by e mail C placing suggestion boxes at random locations in the company s plant and offices d assembling a group with one member from each department and recording the preferences of these employees

In this density curve the shaded area to the left of B is represented by D The shaded area to the right of B is represented by E Match each letter in the density curve with the value it represents Mean D A BC Median Mode 50 of the area

2 8 pts Scott has 8 class periods per week If we let our random variable C the number of classes Scott is on time to in a week the corresponding probabilities are included in the table below Use the table to answer the following questions C P C 0 0 02 1 0 08 2 0 14 3 0 16 4 0 22 5 0 18 6 0 10 7 0 06 8 0 04 a In a random week what is the probability that Scott is on time to exactly 5 classes P 5 P C 5 0 18 b In a random week what is the probability that Scott is on time to at least 5 classes P 5 P 6 P 7 P 8 0 18 0 10 0 06 0 04 0 38 c In a random week what is the probability that Scott is on time to less than 3 classes P 0 P 1 P 2 0 02 0 08 0 14 0 24 d What is the expected number of classes that Scott will be on time to in a week Either show your work or tell me what method of technology you used to solve this Don t forget your units

2 Which method is most likely to produce a random sample of the members of your class a listing the first six students that come to mind b choosing the five oldest students in the class writing the name of each student on a separate piece of paper and then drawing these slips from a hat d selecting the first six students to arrive at class

1 What is the best sampling technique to use for determining the average speed of the cars o section of highway a simple random sample b systematic sample c d convenience sample a or b

Label this graph for a distribution of women s weights standard deviation of 12 lb SD 12 nean 161 eck onel Grou 161 th a m What percent of women weigh between 149 and 173 lb

Given the beam loading shown below select the correct type of function for the internal bending moment diagram between points D and E A 2000 N m B 2 m 2 m Constant horizontal value Quadratic function Cubic function 4 m O Linear function increasing or decreasing D 100 N m 4 m 5 m 250 N F

Given the beam loading shown below select the correct type of function for the internal bending moment diagram between points C and D A 2000 N m B 2 m2 m Quadratic function Cubic function 4 m D O Constant horizontal value O Linear function increasing or decreasing 100 N m 4 m mo 5 m 250 N

List all the permutations of five objects x y z s and t taken two at a time without repetition What is 5P2 List all the permutations of five objects x y z s and t taken two at a time without repetition Choose the correct answer below O A x y z s t OB xx xy xz xs xt yy yz ys yt zz zs zt ss st tt OC xy xz xs xt yz ys yt zs zt st OD xy xz xs xt yx yz ys yt zx zy zs zt sx sy sz st tx ty tz ts What is 5P2 Simplify your answer

List all the permutations of five objects x y z s and t taken two at a time without repetition What is 5P2 List all the permutations of five objects x y z s and t taken two at a time without repetition Choose the correct answer below OA x y z s t O B xx xy xz xs xt yy yz ys yt zz zs zt ss st tt OC xy xz xs xt yz ys yt zs zt st O D xy xz xs xt yx yz ys yt zx zy zs zt sx sy sz st tx ty tz ts What is 5P2 Simplify your answer

possible A player is dealt 6 cards from a standard 52 card deck Determine the probability of being dealt four of a kind such as four aces or four kings by answering questions a through d a How many ways can 6 cards be selected from a 52 card deck There are ways that 6cards can be selected from a 52 card deck Type a whole number b Each deck contains 4 twos 4 threes and so on How many ways can four of the same card be selected from the deck There are ways that four of the same card can be selected from the deck Type a whole number c The remaining 2 cards must be different from the 4 chosen and different from each other After selecting the four of a kind there are 12 different ranks of cards remaining in the deck that can be chosen Of the 12 ranks remaining the player chooses 2 of them and then selects one of the 4 cards in each of the two chosen ranks How many ways can the player select the remaining 2 cards There are ways the player can select the remaining 2 cards Type a whole number A d Use the General Multiplication Rule to compute the probability of obtaining four of kind That is what is the probability of selecting four of a kind and two cards that are not alike The probability of obtaining four of a kind from 6 cards dealt is

possible The data on the right represent the number of live multiple delivery births three or more babies in a particular year for women 15 to 54 years old Use the data to complete parts a through d below Age 15 19 20 24 25 29 30 34 35 39 40 44 45 54 Number of Multiple Births a Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother 30 to 39 years old P 30 to 39 Type an integer or decimal rounded to three decimal places as needed b Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was not 30 to 39 years old P not 30 to 39 Type an integer or decimal rounded to three decimal places as needed 92 505 1630 2832 1847 379 117 c Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was less than 45 years old P less than 45 Type an integer or decimal rounded to three decimal places as needed d Determine the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old Interpret this result Is it unusual Find the probability that a randomly selected multiple birth for women 15 54 years old involved a mother who was at least 40 years old P at least 40 three decimal places as needed

List all the combinations of five objects a b c d and e taken two at a time What is 5C2 List all the combinations of five objects a b c d and e taken two at a time Choose the correct answer below OA a b c d e OB aa ab ac ad ae bb bc bd be cc cd ce dd de ee OC ab ac ad ae ba bc bd be ca cb cd ce da db dc de ea eb ec ed

A family has seven children If this family has exactly three boys how many different birth and gender orders are possible There are different birth and gender orders possible Type a whole number

possible List all the permutations of five objects x y z s and t taken two at a time without repetition What is 5P2 List all the permutations of five objects x y z s and t taken two at a time without repetition Choose the correct answer below O A x y z s t O B xx xy xz xs xt yy yz ys yt zz zs zt ss st tt OC xy xz xs xt yz ys yt zs zt st O D xy xz xs xt yx yz ys yt zx zy zs zt sx sy sz st tx ty tz ts What is 5P2 Simplify your answer

1 Evaluate the expression below given the data set 2 4 6 8 2x 3 Answer Previous Answer 28 Return to overview

List all the combinations of five objects a b c d and e taken two at a time What is 5C2 List all the combinations of five objects a b c d and e taken two at a time Choose the correct answer below OA a b c d e B aa ab ac ad ae bb bc bd be cc cd ce dd de ee C ab ac ad ae ba bc bd be ca cb cd ce da db dc de ea eb ec ed O D ab ac ad ae bc bd be cd ce de What is 5C2 Cimplify your onewer

LES A license plate is to consist of 5 digits followed by 2 uppercase letters Determine the number of different license plates possible if the first and second digits must be odd and repetition is not permitted Choose the correcrt answer below OA 4 368 000 OB 7 370 OC 74 880 000 O D D 6 739 200 000

The following data represent the number of different communication activities used by a random sample of teenagers in a given week Complete parts a through d Activities Male Female Total because 0 22 22 44 because 1 2 81 53 134 a Are the events male and 5 activities independent 3 4 5 58 39 56 69 114 108 because Total 200 200 400 b Are the events female and 0 activities independent are c Are the events 1 2 activities and 5 activities mutually exclusive is are d Are the events male and 1 2 activities mutually exclusive

A lottery exists where balls numbered 1 to 24 are placed in an urn To win you must match the five balls chosen in the correct order How many possible outcomes are there for this game The number of possible outcomes is Simplif

Suppose that E and F are two events and that P E and F 0 1 and P E 0 4 What is P FIE P FIE Type an integer or a decimal

Suppose Emerson loses 30 of all checker games a What is the probability that Emerson loses two checker games in a row b What is the probability that Emerson loses three checker games in a row c When events are independent their complements are independent as well Use this result to determine the probability that Emerson loses three checker games in a row but does not lose four in a row a The probability that Emerson loses two checker games in a row is Round to four decimal places as needed b The probability that Emerson loses three checker games in a row is Round to four decimal places as needed c The probability that Emerson loses three checker games in a row but does not lose four in a row is Round to fo

Suppose that E and F are two events and that P E 0 4 and P FIE 0 8 What is P E and F P E and F Simplify your answer

Given the sample statistics determine if you should use the t distribution normal distribution or neither to construct a confidence interval for an estimate of From a sample of 22 observations the sample mean x bar 267 s 35 o is unknown the data have a bell shaped distribution Ot distribution O Neither Normal distribution

A manufacturer wishes to estimate the proportion of washing machines leaving the factory that is defective How large a sample should she check in order to be 94 percent confident that the true proportion is estimated to within 0 015 O 3928 01 O 32 O 3927

Use the given degree of confidence and sample data to construct a confidence interval for the population mean Assume that the population has a normal distribution A sociologist develops a test to measure attitudes about public transportation and 27 randomly selected subjects are given the test Their mean score is 76 2 and their standard deviation is 21 4 Construct the 95 confidence interval for the mean score of all such subjects O 64 2 88 2 O 67 7 84 7 O 74 677 8

Solve the problem Find the critical value ta 2 that corresponds to a confidence level of 98 and a sample siz of 8 O 2 306 O 2 998 O 2 365

Use the given degree of confidence and sample data to construct a confidence interval for the population mean A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 225 milligrams with 13 4 milligrams Construct a 95 percent confidence interval for the true mean cholesterol content of all such eggs O 222 228 O 223 229 O 221 227 O 221 228

Use the given degree of confidence and sample data to find the margin of error in estimating the population mean Replacement times for washing machines 90 confidence n 30 the sample mean x bar 9 6 years s 2 3 years O 0 1 years O 5 5 years O 0 7 years 05 years

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p Of 100 adults selected randomly from one town 63 have health insurance Find a 90 confidence interval for the true proportion of all adults in the town who have health insurance O 0 518 p 0 742 0 535 p 0 725 O 0 551 p 0 709

You select a family with three children If M represents a male child and F represents a female child the set of equally likely outcomes for the children s genders is MMM MMF MFM MFF FMM FMF FFM FFF Find the probability of selecting a family with 4 male children P 4 male children Type an integer or a simplified fraction WIN