Stat Final all chapters

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 800 tickets. There is one $2,000 grand prize, three $300 second prizes, and fifteen $20 third prizes. You just bought a ticket. Find the expected value for your profit.

-1 (with margin: 0.02) 1995 x 1/800+ 295 x 3/800 + 15 x 15/800 + -5 x 781/800 = -1

E and F are mutually exclusive events. P(E) = 0.3; P(F) = 0.2. Find P(E | F).

0

U and V are mutually exclusive events. P(U) = 0.3; P(V) = 0.2. Find: A. P(U AND V) = B. P(U|V) = C. P(U OR V) =

0 0 0.5

Complete the following probability distribution function table. x P(x) 1 0.3 3 [ ] 7 0.2 12 0.4

0.1

Suppose that you have 11 cards. 5 are red and 6 are black. The cards are well shuffled. You randomly draw two cards with replacement. • R1 = first card drawn is red • R2 = second card drawn is red P(R1 AND R2) = P(At least one red) = P(R2|R1) = Are R1 and R2 independent

0.21 0.70 0.45 yes they are independent

Consider the following scenario: • Let P(C) = 0.7 • Let P(D) = 0.4 • Let P(C|D) = 0.8 A. P(C AND D) = B. Are C and D Mutually Exclusive? C. Are C and D independent events? D. P(C OR D) = E. P(D|C) =

0.32 no no 0.78 0.46

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below: FlossingperWeek Freq RelativeFreq CumulativeRelativeFreq 0 27 0.4500 1 18 3 0.9333 6 3 0.0500 7 1 0.0167

0.9833 (with margin: 0.001) The cumulative relative frequency for 3 time per week is 0.9333. Add in the 0.0500 for 6 times per week gives a cumulative relative frequency of 0.9833.

Suppose that you have 11 cards. 6 are red and 5 are black. The 6 red cards are numbered 1,2,3,4,5 and 6. The 5 black cards are numbered 1, 2, 3,4 and 5. The cards are well shuffled. You randomly draw one card. • R = card drawn is red • E = card drawn is even-numbered How many elements are there in the sample space? P(E)=

11 0.45

A psychologist conducted a study that involved surveying people on whether they were left or right handed and whether they were Shy, Average, or Outgoing. The results are shown in the table below. Shy Average Outgoing Total Left 18 23 12 53 Right 37 52 46 135 Total 55 75 58 188 A. P(Not Average) = B. P(Average OR Outgoing) = C. P(Shy AND Right Handed) = D. P(Left Handed OR Average) = E. P(Right Handed GIVEN Shy) =

133/188 37/188 105/188 37/55

The featured car at the auto dealership comes in three colors: Black, Green, or Blue, and comes with either a Hybrid or Standard engine. The monthly sales of the featured car are shown in the table below. Black Green Blue Total Hybrid 37 28 39 104 Standard66 42 59 167 Total 103 70 98 271 Answer the following and present your answer as a fraction, either using the tallies given or reduced to lowest terms. If a car that was purchased is randomly selected then A. P(Standard) = B. P(Blue) = C. P(Hybrid AND Black) = D. P(Standard OR Green) = E. P(Hybrid GIVEN Blue) =

167/271 98/271 37/271 195/271 39/98

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below: FlossingperWeek Freq RelativeFreq CumulativeRelativeFreq 0 27 0.4500 1 18 3 0.9333 6 3 0.0500 7 1 0.0167

75 (with margin: 0) Since there was a total of 60 adults in the study and 45 flossed at most 1 time per week, we have 45/60 x 100% = 75%

An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on. A. How many elements are there in the sample space? B. Let A be the event that there are at least two tails. P(A) = C. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive?

8 1/2 yes

The statistics below describe the data collected by a business person who researched the amount of money 65 customers spent. mew=27.52 median=24.96 standard deviation=6.34 1st quartile=18.34 3rd quartile=35.72 n=65

A sample of 10 receipts is taken. What is the best prediction for the number of these receipts that were less than $24.96? 5 25% of all receipts were more than how much money? 35.72 25% of all receipts were less than how much money? 18.34 What percent of all the receipts were between $18.34 and 35.72? 50 What is the population standard deviation? 6.34 How many standard deviations below the mean is the first quartile? Round your answer to three decimal places. 1.448

A fitness center is interested in the average amount of time a client exercises in the center each week. Match the vocabulary word with its corresponding example

All clients at the fitness center: Population The 45 clients from the fitness center who participated in the study:Sample The average amount of time that all clients from the fitness center exercise: Parameter The average amount of exercise time for the 45 clients from the fitness center who participated in the study:Statistic The amount of time that any given client from the fitness center exercises: Variable All 45 exercise times there were recorded from the participants in the study: Data

A marriage counselor is interested in the proportion the clients she counsels that stay married. Match the vocabulary word with its corresponding example.

All of the counselor's clients: Population The 55 randomly selected clients that were chosen for this study: Sample The proportion of all of the counselor's clients who stayed married: Parameter The proportion of the 55 randomly selected clients who stayed married: Statistic The answer "Yes" or "No" to the question on whether a client stayed married: Variable The list of "Yes" or "No" answers to the question on whether the clients stayed married: Data

A sheriff is interested in the average speed that people drive on Highway 50. Match the vocabulary word with its corresponding example.

All people who drive on Highway 50: Population The 250 randomly selected drivers who were on Highway 50: Sample The average speed that all drivers go on Highway 50: Parameter The average speed that the 250 randomly selected drivers drove on Highway 50: Statistic The speed that a driver drives on Highway 50: Variable The list of the 250 speeds that the drivers studied drove: Data

A political action committee is interested in the proportion of all registered voters who will vote "Yes" on a measure to expand the use of solar energy. Match the vocabulary word with its corresponding example.

All registered voters in the US: Population The 1000 registered voters who participated in the study: Sample The proportion of registered voters who will vote "Yes" on the measure: Parameter The proportion of the 1000 registered voters that were surveyed who will vote "Yes" on the measure: Statistic "Yes" or "No" for each registered voter:Variable The list of "Yes" and "No" answers that were given by the 1000 participants in the study: Data

A state university is interested in where its students come from. They survey 300 of its students to find out if they are in-state, out-of-state, or foreign students. Match the vocabulary word with its corresponding example.

All students at the university Population The 300 students who were surveyed Sample The proportion of all students from this university who are in-state students Parameter The proportion of the 300 surveyed students who are in-state students Statistic The answer "in-state", "out-of-state", or "foreign" Variable The list of the 300 answers to the survey question Data

Determine if the following is an example of descriptive or inferential statistics. A hospital administrator wants to see if fewer mistakes are made if nurses are forced to take frequent breaks. After observing 300 nurses who were not forced to take frequent breaks and 400 who were forced to take frequent breaks, it was clear from the data that implementing a policy to force nurses to take frequent breaks will decrease the average number of mistakes.

Inferential statistics

Determine if the following is an example of descriptive or inferential statistics. 300 female Osprey hatch-lings were tracked until they died or succeeded in laying their own eggs. Based on the data, the researchers concluded that somewhere between 12% and 18% of all female Osprey hatch-lings in the US succeed in growing up to lay their own eggs.

Inferential statistics is about making conclusions about the population based on the sample.

Answer the following questions and round your answers to 2 decimal places. 13% of all Americans live in poverty. If 45 Americans are randomly selected, find the probability that A. Exactly 5 of them live in poverty. B. At most 5 of them live in poverty. C. At least 5 of them live in poverty. D. Between 3 and 6 (including 3 and 6) of them live in poverty.

Number of trials n = 45 Probability of success p = 0.13 A. To find the probability of "exactly" 5, it is "pdf": binompdf(45,0.13,5)=0.17 B. To find the probability of "at most" 5, it is "cdf": binomcdf(45,0.13,5) = 0.46 C. Since we want the probability of "at least" 5, we use the rule of complements: 1-binomcdf(45,0.13,4) = 0.71 D. Notice the numbers "between 3 and 6" are the numbers less than or equal to 6 but not less than or equal to 2: binomcdf(45,0.13,6)-binomcdf(45,0.13,2) = 0.58

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: #ofCourses Freq RelativeFreq CumulativeRelativeFreq 1 30 0.6 2 15 3 Find the relative frequency for students taking 3 courses.

Since there are a total of 50 Students and 45 are taking 1 or 2 courses, there are 5 left to take 3 courses.5/50 = 0.1

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below: #FlossingperWeek Freq RelativeFreq CumulativeRelativeFreq 0 27 0.4500 1 18 3 0.9333 6 3 0.0500 7 1 0.0167

Since there was a total of 60 adults in the study and 45 flossed at most 1 time per week, we have 45/60 x 100% = 75%

A researcher wants to survey 2000 Americans for an obesity study. Match the strategies to their corresponding sampling techniques.

The researcher makes sure that the proportion of respondents from each state matches the proportion of each state's population to the US population. Stratified Sampling The researcher picks 20 different small groups: a church group, a Democrat club, a student club, etc., each containing 100 people. Then the researcher makes sure that everyone from each group answers the survey question. Cluster Sampling The researcher gets the complete list from the Census Bureau and surveys every 150,000th person on the list. Systematic Sampling The researcher gets the complete list from the Census Bureau and uses a computer to randomly select 2000 people. Simple Random Sampling

If the samples size is much smaller than the population size, say 20 times smaller, then random sampling with replacement and random sampling without replacement are nearly equivalent.

True With a large population size there is a very small chance of duplicating respondents without replacement.

Answer the following True or False: If a business owner, who is only interested in the bottom line, computes the expected value for the profit made in bidding on a project to be -3,000, then this owner should not bid on this project.

True, a negative expected value indicates that if the owner makes several such bids, then an average loss of $3,000 will likely result.

Consider the boxplot below. l___________________________l l l________l : l_________________________l l l_____:____________________l l 3 8 10 20 38

What quarter has the smallest spread of data? Second What is that spread?2 What quarter has the largest spread of data?Fourth Find the Inter Quartile Range (IQR):The IQR is Q3 - Q1 = 20 - 8 = 12. Which interval has the most data in it? 3-10 What value could represent the 53rd percentile? 11

An experiment consists of first rolling a die and then tossing a coin: A. How many elements are there in the sample space? B. Let A be the event that either a 1, 2, 3 or 4 is rolled first, followed by landing tails on the coin toss. P(A) = C. Let B be the event that an even number is rolled, followed by landing tails on the coin toss. Are the events A and B mutually exclusive?

a.12 b.0.33 c.no not mutually exclusive

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes. Who is the fastest runner with respect to his or her class?

rachel

Determine whether the following is an example of a sampling error or a non sampling error. A researcher studied brother-sister pairs to see if there is a difference in IQ scores. Although the researcher made no mistakes in collecting the data, the findings showed that there was a difference when in reality there is no difference in IQ based on gender.

sampling error since the error was due to random chance.

Consider the boxplot below. Boxplot with five point summary: 6,10,19,21,26 What quarter has the smallest spread of data? What is that spread? What quarter has the largest spread of data? What is that spread? Find the Inter Quartile Range (IQR): Which interval has the most data in it? What value could represent the 53rd percentile?

third 2 second 9 11 19-22 20

Which of the following are reasons that a sampling technique may not be scientific. Choose all that apply.

Correct! The sample is not representative of the population. Correct! Self-Selected Sample. Correct! The sample size is too small. Correct! The wording of survey question influences the response.

Which of the following are reasons that a sampling technique may not be scientific. Choose all that apply.

The wording of survey question influences the response. The sample size is too small. The sample is not representative of the population. Self-Selected Sample.

Answer the following questions and round your answers to 2 decimal places. 56% of violent felons in the prison system are repeat offenders. If 32 violent felons are selected at random, find the probability that A. Exactly 16 of them are repeat offenders. B. At most 20 of them are repeat offenders. C. More than 21 of them are repeat offenders. D. Between 15 and 25 (including 15 and 25) of them are repeat offenders. 0.89

Number of trials n = 32 Probability of success p = 0.56 A. To find the probability of "exactly" 16, it is "pdf": binompdf(32,0.56,16) = 0.11 B. To find the probability of "at most" 20, it is "cdf": binomcdf(32,0.56,20) = 0.82 C. Since we want the probability of "more than" 21, we use the rule of complements: 1-binomcdf(32,0.56,21) = 0.10 D. Notice the numbers "between 15 and 25" are the numbers less than or equal to 25 but not less than or equal to 14: binomcdf(32,0.56,25)-binomcdf(32,0.56,14) = 0.89

The average hotel price in Moscow is $216 per night with a standard deviation of $32. The average hotel price in Cancun is $161 per night with a standard deviation of $22. The average hotel price in Bangkok is $100 per night with a standard deviation of $17. A room at the Emerald Hotel in Moscow costs $200 per night, a room at the Ocean View Hotel in Cancun costs $183 per night, and a room at the Emperor Hotel in Bangkok costs $120 per night. Which hotel is more expensive compared to other hotels in its city?

The Emperor Hotel

A special deck of cards has 20 cards. Nine are green, seven are blue, and four are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? B. Let A be the event that a red card is picked first, followed by landing a tail on the coin toss. P(A) = C. Let B be the event that a green or blue is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? D. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?

a. 40 b. 0.1 c.yes they are mutually exclusive d.no they are not mutually exclusive

Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response. Number of tickets sold to a concert.

it is quantitative-discrete because the data contains whole numbers.

Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response. Favorite Baseball Team

qualitative

Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response.

quantitative - discrete because the data contains whole numbers.

Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response.

quantitative and continuous because the value can be any number including fractions and decimals.

Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response.

quantitative and continuous since the value can be any number including fractions and decimals.

If the samples size is much smaller than the population size, say 20 times smaller, then random sampling with replacement and random sampling without replacement are nearly equivalent.

true

Suppose that you are offered the following "deal". You roll a die. If you roll a 1, you win $20. If you roll a 2 or 3, you win $5. If you roll a 4, 5, or 6, you pay $15. A. Complete the PDF Table. List the x values from largest to smallest. x p(x)

x p(x) 20 0.17 5 0.33 -15 0.5 -2.45 Answer 8:If you play many games you will likely win on average about this much. Answer 9:No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

Suppose that you have 8 cards. 5 are green and 3 are yellow. The cards are well shuffled. You randomly draw two cards without replacement. • G1 = first card drawn is green • G2 = second card drawn is green P(G1 AND G2) = P(At least one green) = P(G2|G1) = Are G1 and G2 independent?

0.357 0.89 0.57 no they are dependent

J and K are independent events. P(J | K) = 0.41. Find P(J)

0.41 (with margin: 0)

46% of all statistics classes require an advanced calculator and 38% require the use of a computer that has statistical software. Of the classes that require an advanced calculator, 18% also require the use of a computer. If a statistics course is selected at random find A. P(Advanced Calculator) = B. P(Statistical Software) = C. P(Require an Advanced Calculator and Statistical Software) = D. P(Require an Advanced Calculator GIVEN Require Statistical Software) =

0.46 0.38 0.0828 0.2184

62% of all the town's residents own a dog and 57% own a cat. Of the dog owners 48% also own a cat. If a town resident is chosen at random find A. P(Own a Dog) = B. P(Own a Cat) = C. P(Own a Cat and a Dog) = D. P(Own a Dog GIVEN Own a Cat) =

0.62 0.57 0.2976 0.5221

Q and R are independent events. P(Q) = 0.5 ; P(Q AND R) = 0.4 . Find P(R).

0.8

The histogram below shows the number of times that students in a statistics class have been to London. Check each of the following that are true statements.

A relative frequency histogram would also have the same shape, just a different scale on the vertical axis. This histogram is skewed right. The mean is greater than the median.

Answer the following True or False: If the profit on a raffle ticket has an expected value of -5 dollars, then the most likely outcome of purchasing a raffle ticket is a net loss of $5.

False, the expected value is the expected average if the experiment is run many many times. It doesn't even have to represent a specific outcome at all

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 50% chance of losing the million dollars. The second company, a hardware company, has a 10% chance of returning $4,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $9,000,000 profit, a 80% of no profit or loss, and a 10% chance of losing the million dollars. Order the expected values from smallest to largest.

Hardware, Software, Biotech Software Company: 5,000,000 x 0.1 + 1,000,000 x 0.4 + -1,000,000 x 0.5 = 400,000 Hardware Company: 4,000,000 x 0.1 + 1,000,000 x 0.3 + -1,000,000 x 0.6 = 100,000 Biotech Firm: 9,000,000 x 0.1 + 0 x 0.8 + -1,000,000 x 0.1 = 800,000

Determine if the following is an example of descriptive or inferential statistics. 300 female Osprey hatch-lings were tracked until they died or succeeded in laying their own eggs. Based on the data, the researchers concluded that somewhere between 12% and 18% of all female Osprey hatch-lings in the US succeed in growing up to lay their own eggs.

Inferential Statistics Nice work, inferential statistics is about making conclusions about the population based on the sample.

The histogram below shows the lengths of many spiders found on the forest floor. Histogram with tallest bar in the middle at 7, twice as tall as the many bars symmetrically dropping on the left and right

Since the bulk of the data is between 5 and 9, this range covers around two standard deviations: 4/2 = 2.

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: #ofCourses Freq RelativeFreq CumulativeRelative Freq 1 30 0.6 2 15 3 What percent of students take exactly two courses? (Be sure to write your answer as a percent and not a proportion)

Since there are a total of 50 Students and 15 are taking 2 courses,15/50 x 100% = 30%.

A college administrator wants to survey 250 students that attend her college to see if students are satisfied with the course offerings. Match the strategies to their corresponding sampling techniques.

The administrator stands by the front door of the admissions department and asks the first 250 students who walk in. Convenience Sampling The administrator researches the ethnic make-up of the college and makes sure that the proportion of each ethnic group represented in the sample is the same as the corresponding proportion of that ethnic group at the college. Stratified Sampling The administrator goes into 9 classes from many subject areas and asks all the students in each of these 9 classes. Cluster Sampling The administrator gets the complete list of students at the college and surveys every 50th students on the list. Systematic Sampling The administrator gets the complete list of students at the college and then uses a computer to randomly select 250 students. She then surveys these 250 students. Simple Random Sampling

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows: Sneakers Frequency 1 2 2 5 3 8 4 12 5 12 6 0 7 1

The mean is: 3.775 The median is: 4 The sample standard deviation is: 1.29 The first quartile is: 3 The third quartile is: 5 What percent of the respondents have had fewer than 4 pairs of sneakers? 37.5 % 67.5% of all respondents have had at most how many pairs of sneakers? 4

Twelve teachers attended a seminar on mathematical problem solving. Their attitudes were measured before and after the seminar. A positive number change attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows: 3, 8, -1, 2, 0, 5, -3, 1, -1, 6, 5, -2

The mean is:1.92 The sample standard deviation is: 3.50 The first quartile is:-1 The median is:1.5 The third quartile is:5 Find the change score that corresponds to 3 standard deviations above the mean. 12 If a teacher experiences a change score of 4, how many standard deviations above the mean is this score? 0.59

The histogram below shows the distribution of a recent exam. Check true statements.

This histogram is skewed left. A relative frequency histogram would also have the same shape, just a different scale on the vertical axis. The median is greater than the mean.

Determine whether the following is an example of a sampling error or a non sampling error. 12% of all people are left handed. A researcher randomly selected 200 people and found that 16% of them were left handed. No mistakes were made in the data collection or data recording. The 4% difference is due to ...

This is an example of sampling error, since the error was due to random chance.

Roll two fair dice. Each die has six faces. A. Let A be the event that either a 4 or 5 is rolled first followed by an even number. P(A) = B. Let B be the event that the sum of the two dice is at most 5. P(B) = 0.17 Round your answer to two decimal places. C. Are A and B mutually exclusive events? D. Are A and B independent events?

a.0.17 b.0.28 c.yes d.they are dependent events