Statistics Questions and Answers

DEN SCHR Question 3 Multiple Choice Warth 3 points Federal Income Taxes and Piecewise Functions LC The graph of a piecewise function is shown 7 6 5 4 01 00 00 3 07 0 00 2 What is the domain of the function Q 6 40 st 4 3 2 d 1 N 3 4 5 6 History Lombar 2 3 4 5 6

Two Way Frequency Tables MC A sample of 80 high school drama club and art club students were surveyed to choose a favorite free time activity playing computer games listening to music or watching movies TV 50 of the sample is drama club students From the sample it is found that 25 were drama club students who prefer listening to music and 20 were drama club students who prefer watching movies TV 18 75 were art club students who prefer playing computer games while 15 were art club students who prefer listening to music 40 of the students surveyed chose listening to music Which of the following is a correct two way relative frequency table for the data O Drama Club Students Art Club Students Column Totals O Drama Club Students Art Club Students Column Totals Drama Club Students Art Club Students Column Totals Drama Club and Art Club Leisure Time Activity Preferences Playing Computer Games 5 18 75 23 75 18 75 23 75 15 Listening to Music Watching Movies TV Row Totals 50 20 16 25 50 36 25 Drama Club and Art Club Leisure Time Activity Preferences Playing Computer Games Listening to Music Watching Movies TV Row Totals 5 50 50 100 19 25 15 40 Drama Club Students 5 25 15 40 Drama Club and Art Club Leisure Time Activity Preferences Playing Computer Games Listening to Music Watching Movies TV 4 20 12 15 16 25 32 38 25 16 13 100 29 Row Totals 40 40 80 Drama Club and Art Club Leisure Time Activity Preferences Playing Computer Games Listening to Music Watching Movies TV Row Totals 25 15

Evaluating Reports MC A set of data is represented in the stem plot below 3456789 5 2 1 8 4 5 5 6 5 8 8 6 7 Key 315 35 Part A Find the mean of the data Show each step of work 2 points Part B Find the median of the data Explain how you determined the median 2 points Part C Find the mode of the data Explain how you determined the mode 2 points Part D Compare your values for mean median and mode from parts A B and C Which value would best represent the data and why Explain using complete sentence 2X Source C SO

Two Way Frequency Tables LC Students on the soccer team and the rugby team at several high schools were surveyed to choose a vacation location Aspen Colorado or New York New York Which location would you most like to visit Soccer team students 22 Rugby team students 16 Column totals 38 O 28 O 34 Which location would you most like to visit Aspen Colorado O 50 62 New York New York Row totals 28 34 62 What is the joint frequency of soccer team students who would most like to visit New York 50 50 100

7 6 5 Winning 4 Time 3 2 1 0 y 0 1 1 52 minutes O 1 98 minutes Predict the winning time in year 10 of the race O2 83 minutes 2 3 01 minutes 3 4 5 Time Years 6 7 8 X 9

Linear Functions Fit to Data MC A hair salon owner collected data comparing the length of an appointment in hours at the salon and the amount of money spent by the customer The data shown in the table is represented in the graph Use the table and the graph of the data to answer the questions Amount of Money Spent dollars 225 Hair Salon 200 175 150 125 100 75 50 25 0 1 2 3 Time hours 4 0X Source C X 3 4 BIUS X xI Styles Format Part A Determine the equation for the line of fit Show all work and include all steps 4 points Part B Identify and interpret the slope in the context of this scenario 3 points Part C Demonstrate how to use your equation for the line of fit from Part A to predict the cost of a 6 hour hair salon appointment Show all work and include all steps 3 points F Font Size Hours Money Spent 25 AA 1 1 1 5 1 75 2 2 2 5 3 3 3 5 4 4 5 30 45 50 55 60 75 85 90 105 120 125

Linear Functions Fit to Data LC A professional bowler wanted to gather data about the cost of local bowling leagues in the area After collecting and plotting the data it was determined that the average bowling league consists of a one time registration fee and a monthly fee modeled by the equation 12x 30 Identify and interpret the slope in this scenario O The slope is 30 Starting at 12 the cost will increase by 30 per month O The slope is 30 Starting at 12 the cost will decrease by 30 per month The slope is 12 Starting at 30 the cost will increase by 12 per month O The slope is 12 Starting at 30 the cost will decrease by 12 per month

A student recorded the different types of pizza their friends like in the table below Pizza Type Number of Friends Cheese 2 Mushroom 4 Pepperoni 1 Supreme 3 Which of the following plots represents the data in the table O Chivete Cheese Mushroom Popporoni Supreme Types of Pizza 0 Pizza Chease Pizza 0 Mushroom Papperoni Supreme Types of Pizza Pizza Mushroom Popperoni Supreme Types of Pizza Pizza O Cheese Mushroom Pepperoni Supreme Types of Pizza

High school students grade point averages are listed in a data set Which of the following charts could be used to display the data and why Box plot because the data is categorical O Box plot because the data is numerical O Circle graph because the data is categorical O Circle graph because the data is numerical

Use the histogram of Investment Account Values to answer the question Number of Investments 10 9 8 7 6 5 4 3 210 25 64 39 Investment Account Values O 32 50 00 100 00 150 00 What percentage of investments have a value over 150 Account Values 200 00 250 00

Use the stem and leaf plot of Monthly Sales Goals to answer the question that follows Monthly Sales Goals in thousands 1 2 3 4 Stem O 18 000 O 22 000 O 30 000 89 O 40 000 5668 What is the range of the monthly sales goals Leaf 23369 0

4 reflection across y 1 Ay W Z

Example used that covers material in Chapter 1 Section 2 think this would make a good test question because learning the difference between quantitative and qualitative data types is a foundational component of statistics A supermarket is stocking up on vegetables they recently received a shipment of 11 carrots 15 jalapenos and 25 bell peppers Determine the correct data type quantitative or or qualitative for the total number of vegetables received A Quantitative B Qualitative C Neither A or B D Both A B

12 Speed Dating Use these female measures of male attractiveness given in Exercise 18 Speed Dating in Section 7 2 on page 329 5 8 3 8 6 10 3 7 9 8 5 5 6 8 8 7 3 5 5 6 8 7 8 8 8 7 Use the bootstrap method with 1000 bootstrap samples a Construct a 99 confidence interval estimate of the population mean Is the result dramati cally different from the 99 confidence interval found in Exercise 18 in Section 7 2 b Construct a 95 confidence interval estimate of the population standard deviation Is the result dramatically different from the 95 confidence interval found in Exercise 14 Speed Dating in Section 7 3 on page 340

8 Walter and Carl both often need to travel from Location A to Location B Walter walks and his travel time is Normal with mean w minutes and standard deviation o minutes travel time can t be negative without using a tachyon beam but assume that w is so much larger than o that the chance of a negative travel time is negligible Carl drives his car and his travel time is Normal with mean c minutes and standard deviation 20 minutes the standard deviation is larger for Carl due to variability in traffic conditions Walter s travel time is independent of Carl s On a certain day Walter and Carl leave from Location A to Location B at the same time a Find the probability that Carl arrives first in terms of and the parameters For this you can use the important fact proven in the next chapter that if X and X are independent with X N 0 then X X N 1 2 0 02 b Give a fully simplified criterion not in terms of such that Carl has more than a 50 chance of arriving first if and only if the criterion is satisfied c Walter and Carl want to make it to a meeting at Location B that is scheduled to begin w 10 minutes after they depart from Location A Give a fully simplified criterion not in terms of such that Carl is more likely than Walter to make it on time for the meeting if and only if the criterion is satisfied

6 a Freddy has a lot of cousins Some of his co words to Bohemian Rhapsody and some ca Draw a labelled Venn diagram to represent

6 a Freddy has a lot of cousins So words to Bohemian Rhapsody Draw a labelled Venn diagram t

Which data set has the greatest spread Set A 84 91 87 77 94 89 74 Set B 89 73 84 91 87 77 94 Set C 73 84 89 88 77 91 87 90 Set D 84 89 88 82 91 87 99

A study was conducted to determine if the amount a college student spends per month on recreation is related to the student s income 901 1037 985 260 243 289 Monthly income x Amount y r0 996 Part 0 3 Part 1 of 3 925 253 ris not is This not 600 121 a Find the equation of the regression line and draw the line on the scatter plot Round the slope and y intercept to at least four decimal places if necessary significant at the 5 level 1061 296 regression line is y 0 X 1256 386 X

A researcher hopes to determine whether the number of hours a person jogs per week is related to the person s age Age x Hours y 20 47 6 2 5 43 21 54 2 5 5 1 5 r 0 982 Part 0 3 Part 1 of 3 Find the equation of the regression line and draw the line on the scatter plot but only if r is significant Round the slope and y intercept to four decimal places If necessary r Choose one significant at the 5 level F X

7 8 9 5 10 Step 2 of 2 Determine the relative frequency for the fourth class as a simp Answer

Consider the following frequency table representing the de

me Left 0 09 14 It is time for Roger Hall manager of new car sales at the Maxwell Ford dealership to submit his order for new Mustang coupes These cars will be parked in the lot available for immediate sale to buyers who are not special ordering a car Roger must decide how many Mustangs of each color he should order The new color options are very similar to the past year s options Roger believes the colors chosen by customers who special order their cars best reflect most customers true color preferences He has taken a random sample of 60 special orders for Mustang coupes placed in the past year The color preferences found in the sample are listed below Black Sarah Pritchett Attempt 1 Color of Car Frequency Blue pui Green Red 15 8 6 24

The closing prices in pence for selected stocks trading on the London Stock Exchang the following class limits 0 199 200 399 400 599 600 799 800 999 Stock Closing Pr Reliance Infrastructure Etalon Group Tufton Oceanic PJSC LSR Group Hon Hai Precision TMT Investments Sistema Mahindra Mahindra Ltd O Key Group Integrated Diagnostics GAIL India Ltd JPEL Private Equity Terracon Financial Group

stion 1 an U S income According to the U S Census Bureau the

When dragons on planet Pern lay eggs the eggs are either green or yellow The biologists have observed over the years that 19 of the eggs are yellow and the rest green Next spring the lead scientist has permission to randomly select 41 of the dragon eggs to incubate Consider all the possible samples of 41 dragon eggs What is the mean number of yellow eggs in samples of 41 eggs that is the same as asking for the expected value of the number of yellow eggs Give answer correct to at least one decimal place mean What is the standard deviation in the number of yellow eggs in samples of size 41 Give answer correct to at least one decimal place standard deviation What is the variance in the number of yellow eggs in samples of size 41 Remember to calculate the answer using at least 5 decimal places then give answer correct to at least one decimal place variance

X P x 0 0 05 1 0 25 2 0 2 3 0 5 Find the standard deviation of this probability distribution Give your answer to at least 2 c places

Previous For the data shown answer the questions Round to 2 decimal places X 19 6 19 2 13 6 7 2 1 9 4 3 12 8 22 2 10 14 1 Find the mean Find the median Find the standard deviation

About 5 of the population has a particular genetic mutation 900 people are randomly selecte Find the mean for the number of people with the genetic mutation in such groups of 900

Given the following data 44 13 47 58 49 37 45 35 55 36 57 58 32 45 30 27 36 45 51 72 55 66 79 79 57 41 60 45 24 81 48 53 82 26 33 54 35 22 33 63 78 66 35 47 18 58 64 54 68 42 a From the raw data compute the mean the median and the mode b Obtain a grouped frequency distribution to compute the mean the median and the me and compare the results with those in Question a above c From the raw data compute the first quartile the fourth decile seventy fifth percent In each case explain the significance of the answer d From the grouped frequency distribution compute the first quartile the fourth deci seventy fifth percentile and compare the results with those in Question c above

An invesurient company advertised that last year its clients on average made a profit of 8 Assuming that average refers to the mean which of the followin claims must be true based on this information Note More than one statement could be true If none of the statements is true mark the appropriate box n Two years ago at least one of their clients made a profit of at least 8 Last year some of their clients made a profit of exactly 8 Last year the number of their clients who made a profit of 8 or less was equal to the number of their clients who made a profit of 8 or more Last year at least one of their clients made a profit of at least 8 Last year all of their clients made a profit of more than 2 None of the above statements are true x

Last month 4 customers of Macland Automotive bought the extended service plan with their purchase of a new car All of their credit scores are given below Calculate the standard deviation of this population data Round your answer to 2 places after the decimal point if necessary X 752 1 759 1 766 7 797 2 standard deviation

Calculate the mean and sample standard deviation of the data shown Round to two decimal places X 9 1 10 4 15 5 18 3 28 3 mean 16 32 Sample standard deviation

Fitting a straight line to a set of data a Should this model be used to pre b Should this model be used to pre c Should this model be used to pre d Should this model be used to pre a Should this model be used to pre O Yes

K You are testing the null hypothesis that there is no linear relationship between two variable a What is the value of tSTAT b At the 0 05 level of significance what are the critical values c Based on your answers to a and b what statistical decision should you make d Construct a 95 confidence interval estimate of the population slope B a What are the hypotheses to test O A Ho B 0 H B 0 O C Ho B 20 H B 0 tSTAT Round to two decimal places as needed b The lower critical value is The upper critical value is Round to four decimal places as needed c What statistical decision should you make

A business magazine was conducting a study into the amount o number of days they spent traveling each year

Consider the following frequency table representing th

A business magazine was conducting a study in days they spent traveling each year

5 The figure below shows a pole OF with two arms parallel to the ground extending toward points A and C respectively The pole is supported by two cables AB and CD The magnitudes of the tension forces TAB and Tcp are 3 4 kN and 5 6 kN respectively Use the vector method of computing moments in this problem Hint you can use your solutions to Homework 2 Question 2 to help simplify this problem a Calculate the resultant moment of these two forces about the origin b Find the component of the resultant moment perpendicular to the pole OF 3 1 2 m TAB 60 cm F 20 cm B 1 2 m 70 cm 1 5 m TCD D 28 80 cm E y

The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short 1 2 pages medium 3 4 pages or long 5 6 pages Data on recent reviews indicates that 60 of them are short 30 are medium and the other 10 are long Reviews are submitted in either Word or LaTeX For short reviews 80 are in Word whereas 60 of medium reviews are in Word and 40 of long reviews are in Word Suppose a recent review is randomly selected a What is the probability that the selected review was submitted in Word format b If the selected review was submitted in Word format what are the posterior probabilities of it being short medium or long Round your answers to three decimal places short medium long

A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate The survey reported a confidence interval that between 64 5 and 69 5 of the population preferred Candidate A What is the margin of error on the survey Do not write on the margin of error

The Central Intelligence Agency CIA has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages In standard English text the letter s is used at a rate of 5 74 Find the mean and standard deviation for the number of times the letter s will be found on a typical page of 2100 characters Round solutions to three decimal places if necessary Hint This is a Binomial experiment l

A pizza parlor offers a choice of 13 different toppings How many 3 topping pizzas are possible Should this exercise involve permutations combinations or the fundamental counting principle Fundamental Counting Principle Combinations Permutations There are possible 3 topping pizzas

4 A school nurse measured the heights of all 15 year old male students in the school By the end of the day he measured the heights of 57 boys and calculated a mean of 68 1 inches He knows that for this population 67 inches and o 3 19 inches a Calculate the z score for the sample mean b Is it likely or unlikely that this sample was drawn from the population c Why or why not

3 You are conducting a z test on a sample of 132 people for whom you observed a mean verbal score on the SAT a university admissions test of 490 The population mean is 500 and the population standard deviation is 100 a Calculate the z score for that sample mean b Is it likely or unlikely that this sample was drawn from the population c Why or why not

What is the standard size of the critical region used by most statisticians

Students want to test the claim that a bag of their favorite potato chips weighs 30 0 grams on average They collect 5 random bags of these potato chips and carefully weigh the contents of each bag The standard deviation of the weights was found to be 0 663 grams Here is their recorded data in grams 28 9 29 8 30 4 28 8 29 6

Age Men Women 16 24 25 34 35 44 45 54 458 424 715 916 634 709 16 24 25 34 a Use the data to make a 6 x 2 matrix with each row representing an age cate Men Women 35 44 967 45 54 55 64 712 55 64 65 965 791 727 602

The vertex adjacency matrix for graph G is shown below 0 1 0 0 1 0 0 10 0 0 0 1 0 0 1 01 0 100 00 1 0 10 0 0 101 00 1 0 0 0 0 0 0 010 0 10 1 001 0 1 0 0 0 0 1 0 1 0 1 00 100 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 b G is a regular graph Answer Select c G is a bipartite graph Answer Select For each of the characteristics listed below select True in the answer box if the characteristic is applicable to the graph Otherwise select Fal a G is a connected simple graph Answer Select d G is an Eulerian graph Answer Select 0 0 00 e G is semi Eulerian Answer Select 1 0 0 1 0 0 0 0 0 1 0 0 1 0 f G contains a Hamiltonian cycle Answer Select g G has at least one hundred spanning trees Answer Select

Evaluate the following time diagram in terms of life annuity symbols model and model star cut off point at 50