Statistics Questions and Answers

K Use six intervals starting with 0 24 Perform the following a Group the data as indicated b Prepare a frequency distribution with a column for intervals and frequencies c Construct a histogram d Construct a frequency polygon a Tally the given data falling into each interval Choose the correct table below OA OB Interval 0 24 24 48 48 72 H 72 96 96 120 120 149 Tally Will 441 Interval 0 24 25 49 50 74 411 75 99 Hi 100 124 III 125 149 Tally O C Interval 0 24 24 48 48 72 72 96 96 120 120 149 1 Tally 441 1 17 118 115 71 129 25 28 44 127 82 57 136 45 73 63 143 77 72 122 11 46 35 83 82 2 97 84 96 91 36 85 147 32 82 12 101 O D Interval Tally 0 24 Willl LH1 25 49 50 74 75 99 LH1 LH1 IIII 100 124 1 125 149 IIII

Emerald Bazaar has a materials price standard of 2 00 per pound Six thousand pounds of materials were purchased at 2 20 a pound The actual quantity of materials used was 6 000 pounds although the standard quantity allowed for the output was 5 400 pounds Emerald Bazaar s materials price variance is

nd the range and standard deviation for the set of numbers 110 123 141 143 147 196 ne range is

peak in a normal curve appears directly above in the blank below peak in a normal curve appears directly above the standard deviation the z score x equals 1

Find a z score satisfying the following condition 0 of the total area is to the right of z Click here to view page 1 of the Areas under the Normal Curve Table Click here to view page 2 of the Areas under the Normal Curve Table Round to the nearest hundredth as needed

Chebyshev s Theorem states that for any set of numbers the fraction that will lie within k standard 1 deviations of the mean is at least 1 Use this theorem to find the fraction of all the numbers of a data set that must lie within 3 standard deviations from the mean At least of all numbers must lie within 3 standard deviations from the mean Type an integer or a fraction

a Let X be an exponential random variable with a parameter 0 Show that XX is an exponential random variable of parameter 1

Consider two normal distributions one with mean 11 and standard deviation 3 the other with mean 14 and standard deviation 3 Answer the following statements using true or false a The two distributions have the same shape answer b The two distributions are centered at the same place answer Note You can earn partial

5 1 point Let p z be the density function given by Find the mean value of p z p z 0 if 0 z 13 if 13 23 otherwise

Laticia randomly selected 25 of the seventh grade students in her school and asked them their favorite season Of the students surveyed 51 chose summer as their favorite season Based on the data what is the most reasonable prediction of the number of students in her school who would choose summer as their favorite seventh grade season A B C D 15 75 150 200

1 point Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with 106 and o 24 a What proportion of children aged 13 to 15 years old have scores on this test above 92 NOTE Please enter your answer in decimal form For example 45 23 should be entered as 0 4523 Answer 0 6445 b Enter the score which marks the lowest 20 percent of the distribution Answer 78 3 c Enter the score which marks the highest 15 percent of the distribution Answer 135 6

Using diaries for many weeks a study on the lifestyles of visually impaired students was conducted The students kept track of many lifestyle variables including how many hours of sl obtained on a typical day Researchers found that visually impaired students averaged 8 88 hours of sleep with a standard deviation of 2 55 hours Assume that the number of hours c sleep for these visually impaired students is normally distributed a What is the probability that a visually impaired student gets less than 6 4 hours of sleep 4 answer b What is the probability that a visually impaired student gets between 6 9 and 8 6 hours of sleep answer c Twenty percent of students get less than how many hours of sleep on a typical day answer hours

0 Yaster Outfitters manufactures and sells extreme cold sleeping bags The table below shows the price demand and total cost data where M p is the wholesale price in dollars of a sleeping bag for a weekly demand of a sleeping bags C is the total cost in dollars of producing a sleeping bags sleeping bags p 240 235 155 50 95 120 180 220 C 13 000 14 300 18 500 21 000 Use this data to create regression models to answer all of the questions below Price Model Find a quadratic regression equation for the price demand data using as the independent variable pa ba c Round a to the nearest integer round b to 2 decimal places and round c to 4 decimal places Use this price model to answer question 1 2 below

In a random sample 15 people working for a startup technology company were asked about the number of hours they spent exercising during the previous month Their answers were as follows in hours 36 22 28 29 40 33 37 39 40 34 21 39 40 38 and 36 Find the mean and the range for the sample Estimate your answers to 1 decimal place Find the standard deviation and the median for the sample Estimate any irrational answers to two decimal places

Consider two normal distributions one with mean 10 and standard deviation 3 the other with mean 14 and standard deviation 2 Answer the following statements using true or false a The two distributions have the same shape answer b The two distributions are centered at the same place answer

Each hour for several hours the owner of a bakery recorded the number of customers who entered the store The box and whisker plot sometimes called a boxplot summarizes the data 10 15 20 25 30 Number of customers 35 40 45 D 50 Use the box and whisker plot to answer the following a What is the median number of customers 0 b What is the smallest number of customers 0 c What is the first quartile Q of the numbers of customers X

ubian goats of 35 Nubian goats and record the birth weights Assume it is known that the population standard deviation of the birth weights of Nubian goats is 1 36 kg Based on your sample follow the steps below to construct a 90 confidence interval for the population mean of the birth weights for all Nubian goats If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 35 Nubian goats Take Sample Sample size 0 Point estimate 0 Population standard deviation Critical value 0 Compute 0 00 Number of goats Sample mean 0 00 Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute 35 2 00 4 31 Standard error Margin of error 4 00 Sample standard 90 confidence interval 90 confidence interval deviation 1 13 6 00 X b Based on your sample enter the lower and upper limits to graph the 90 confidence interval for the population mean of the birth weights for all Nubian goats Confidence level 99 95 90 Population standard deviation 1 36 8 00 Critical value 20 005 2 576 1 960 20 025 20 050 1 645 10 00 10 00

Your employer offers a 401 k plan with a 27 match and you set a goal of retiring in 31 years with an amount of money which has the same buying power that 1 6 million dollars has today If the account earns an annual interest rate of 1 and the expected annual rate of inflation is 1 1 how much should YOU contribute each month to the 401 k Round your answer to the nearest dollar

Refer to the data table below Complete parts a through d Click on the icon to view the data table a Find the best regression equation with IQ score as the response variable Use predictor variables of brain volume VOL and or weight W Select the correct choice and fill in the answer be complete your choice Round to four decimal places as needed OA A IQ VOL W OB IQ O C 1Q W VOL IQ Brain Volume and Weight Data Table IQ 96 90 87 88 101 103 104 97 127 126 102 95 92 87 94 85 96 115 112 Brain Volume cm 1004 962 1036 1026 1281 1271 1051 1077 1036 1068 1173 1078 1067 1103 1345 1437 1028 1098 1205 Body Weight kg 57 914 58 809 64 942 58 803 63 659 61 002 132 957 107 286 62 806 83 574 61 679 61 526 83 699 79 996 97 542 99 727 81 153 88 823 79 914 X

Use the given data set to complete parts a through c below Use 0 05 13 8 8 14 8 75 X y Click here to view a table of critical values for the correlation coefficient a Construct a scatterplot Choose the correct graph below A 10 9 13 AY 10 8 6 4 2 04 0 0 0000 4 8 12 16 B Ay 10 8 6 4 2 0 9 8 77 4 12 16 Q G 11 9 26 14 8 11 C Ay 10 8 6 4 2 0 4 6 6 13 8 12 16 Q 4 3 09 12 9 14 OD Ay 10 8 6 4 2 0 0 4 8 b Find the linear correlation coefficient r then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables The linear correlation coefficient is r Round to three decimal places as needed 7 7 26 X 12 16 Q Q

A Suppose IQ scores were obtained for 20 randomly selected sets of couples The 20 pairs of measurements yield x 97 76 y 94 9 r 0 832 P value 0 000 and y 6 86 0 9x where x represents the IQ score of the husband Find the best predicted value of y given that the husband has an IQ of 95 Use a significance level of 0 05 Click the icon to view the critical values of the Pearson correlation coefficient r The best predicted value of vis

Heights cm and weights kg are measured for 100 randomly selected adult males and range from heights of 136 to 191 cm and weigh of 40 to 150 kg Let the predictor variable x be the first variable given The 100 paired measurements yield x 167 50 cm y 81 51 kg r 0 342 P value 0 000 and y 105 1 05x Find the best predicted value of y weight given an adult male who is 176 cm tall Use 0 01 significance level Click the icon to view the critical values of the Pearson correlation coefficient r The best predicted value of y for an adult male who is 176 cm tall is Round to two decimal places as needed kg

3 When Hannah wakes up on time there is a 10 chance she will miss the bus for school If she oversleeps there is a 50 chance she will miss the bus On average Hannah oversleeps one morning a week a What is the probability that Hannah will wake up late and miss the bus b What is the probability that Hannah will miss the bus SCHOOL BUS

mal curve Those with z scores above 2 2 will receive an A those between 2 2 and 0 8 will receive a B those between 0 8 and 0 9 will receive a C those between 0 9 and 2 2 will receive a D and those under 2 2 will receive an F Determine the percent of grades that will be A B C D and F Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table 1 39 of the grades are A s Round to two decimal places as needed 19 8 of grades are B s Round to two decimal places as needed 60 4 of grades are C s Round to two decimal places as needed 17 02 of grades are D s Round to two decimal places as needed of grades are F s Pound to two decimal places as needed

A computer randomly selects a number from 1 through 50 Two selections are made by the computer to create an ordered pair of numbers How many elements are in the sample space for this experiment Select one Oa 2500 b 100 C 50 Od 2450 e 2000

Assume the annual day care cost per child is normally distributed with a mean of 8000 and a standard deviation of 1400 What percent of day care costs are more than 8700 annually Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table Round to two decimal places as needed

1 The table shows the number of turtles hatched at a zoo each year since 2003 a Find the line of best fit b Predict the number of turtles to be hatched in 2011 c Estimate the Turtles Hatched Year 2003 21 2004 17 2005 16 2006 2007 16 14

A poll showed that 48 out of 120 randomly chosen graduates of California medical schools last year intended to specialize in family practice What is the width of a 90 percent confidence interval for the proportion that plan to specialize in family practice Multiple Choice SHEBREONE O O 0736 1 0447 0894 1 0876

4 51 Pitchers The table shows the number of wins and the num ber of strike outs SO for 40 baseball pitchers in the major leagues in 2011 Source 2011 MLB PITCHING STATS http www baseball reference com leagues MLB 2011 pitching leaders shtml accessed via StatCrunch Owner IrishBlazeFighter a Make a scatterplot of the data and state the sign of the slope from the scatterplot Use strike outs to predict wins b Use linear regression to find the equation of the best fit line Insert the line on the scatterplot using technology or by hand c Interpret the slope d Interpret the intercept and comment on it Wins 21 19 17 24 18 13 13 14 16 11 21 12 13 15 16 13 19 13 16 16 SOS 248 220 238 250 198 139 220 194 225 146 198 179 175 178 206 117 230 161 197 192 Wins 12 13 16 8 10 9 9 11 14 14 11 14 9 15 16 11 12 13 17 13 SOS 158 191 158 134 197 123 96 178 111 126 191 222 185 182 169 166 218 126 207 158

The data to the right represent the cost of living for 20 states The cost of living is a measure of the average price paid for housing utilities groceries healthcare transportation and miscellaneous expenses The national average cost of living is 100 The data can be used to compare a state to the national average and to other states Cost of living 88 0 99 9 100 0 111 9 112 0 123 9 124 0 135 9 136 0 147 9 148 0 159 9 1 1 20 Type integers or decimals Do not round Number of states 12 1 2 2 160 0 171 9 162 6127 3100 2 95 4 90 60 150 6123 1 97 8 94 2 90 4 135 5119 4 95 7 92 4 89 8 131 6104 5 95 6 91 2 89 7

The accompanying data represent the approximate population in millions of the 20 most populous cities in the world Use these data to construct a frequency distribution with a first class of 6 5 7 5 Fill in the missing classes and the frequency for each class below Population millions of people 6 5 7 5 9 8 10 8 10 9 11 9 Number of Cities 13 3 12 6 10 1 8 4 7 8 13 3 12 1 9 3 8 2 7 8 12 9 10 9 8 9 7 9 7 6 12 7 10 3 8 5 7 9 7 3 00

4 6 Comparing Salaries The scatterplot shows the salary and year of first employment for some professors at a college Explain in context what the negative trend shows Who makes the most and who makes the least Source Minitab Student 12 Salary Salary thousands of dollars per year 100 90 80 70 60 50 40 HA 1985 1990 1995 2000 2005 2010

In general round z scores to 2 decimal places and probabilities to 4 decimal places 1 As part of a study of property values in Minneapolis an appraisal company chose a random sample of 40 apartment buildings and determined each building s age as of January last year The ages in years of the buildings are listed below 83 60 71 70 20 72 63 22 67 19 52 73 23 19 68 19 20 22 73 65 54 33 66 67 51 83 13 14 51 59 72 64 87 80 70 57 83 19 85 76 a Use your calculator functions to determine the sample mean and sample standard deviation Round each to two decimal places 3 pts b Use the results of a to construct a 99 confidence interval estimate of the mean age of apartment buildings in Minneapolis Round the margin of error and bounds to two decimal places 6 pts

SECTION 4 1 1 Predicting Land Value Both scatterplots concern the ssessed value of land with homes on the land and both depict he same observations a Which do you think has a stronger relationship with value of the land the number of acres of land or the number of rooms in the homes Why b If you were trying to predict the value of a parcel of land on which there is a home in this area would you be able to make a better pre diction by knowing the acreage or the number of rooms in the house Explain Source Minitab File Student 12 Assess J Value of Land thousands of dollars s of dollars Value of Land thousands 140 120 100 80 60 40 140 120 100 80 60 40 1 2 3 Acreage 4 5 5 0 7 5 10 0 12 5 15 0 17 5 Rooms 6 2 Predicting Total Value of Property Both scatterplots con n the total assessed value of properties that include homes and th depict the same observations a Which do you think has a stronger relationship with value of the prop erty the number of square feet in the home shown in part B of the figure or the number of fireplaces in the home shown in part A of the figure Why If you were trying to predict the value of a property where there is a home in this area would you be able to make a better prediction by knowing the number of square feet or the number of fireplaces Explain A B Value of Car dollars Total Value thousands of dollars 6000 4000 2000 0 4 0 Total Value thousands of dollars 16000 14000 12000 10000 8000 3 5 3 0 2 5 500 2 0 400 300 200 100 500 400 300 4 3 Car Value and Age of Student The scatterplot show age of students and the value of their cars according to the l Blue Book Does it show an increasing trend a decreasing ta very little trend Explain 200 100 0 500 1000 1500 2000 2500 3000 3500 Number of Square Feet 1 J 1 2 3 4 5 6 Number of Fireplaces 20 25 4 4 Shoe Size and GPA The figure shows a scatterplot of size and GPA for some college students Does it show an incre trend a decreasing trend or no trend Is there a strong relation 30 35 Age of Student 40 45 50

3 58 of students at a certain college are fernale A random sample of 50 students is to be selected Let the random variable X be the number of female students in a sample Round to 4 decimal places a What is the probability that exactly 49 of the students are female 4 pts b What is the probability that 30 or fewer of the students are female 4 pts

RY 4 5 Weight Loss Example 1 The scatterplot shows the actual weight and desired weight change of some students Thus if a student weighed 220 and wanted to weigh 190 the desired weight change would be negative 30 Explain what you see In particular what does it mean that the trend is negative esired Change in Weight pounds 20 10 0 10 20 30 40 50 60 70 100 120 140 160 180 200 220 240 260

Women s Median dollars per yea 50000 45000 40000 35000 30000 3 40000 50000 60000 70000 80000 Men s Median Pay dollars per year b Use the regression equation above the graph to get a more precise estimate of the median pay for women in a state that has a median pay for men of 60 000 4 32 Home Prices and Areas of Four Bedroom Homes a Using the graph estimate the predicted price for a home with 3000 square feet b Use the equation to predict the price for a home with 3900 square feet CHAPTER 4 To do parts a c assume that the The regression equation is 5 67 0 998 X and height is linear a Report the regression equation using the words Height and Armspan not x and x employing the output given b Verify the slope by using the formula br c Verify the y intercept using a 3 bi d Using the regression equation predict the armspan in centimeters for someone 64 inches tall 4 34 Hand and Foot Length for Women The computer out put shown below is for predicting foot length from hand length in cm for a group of women Assume the trend is linear Summary statistics for the data are shown in the table below Hand x Foot y Mean 17 682 23 318 Standard Deviation REGRESSION ANALYSIS EXPLORING ASSOCIATIONS BETWEEN VARIABLES y a bx E HORMAL FLOART AUTO REAL RADIAN HP 0 LinReg 1 168 1 230

Count the number of F s in the following sentence Finished files are the result of years of scientific study combined with the experience of years There are F s

Expand the given function in a Fourier series Give the Fourier series that is the periodic extension off with period 2r f x x 0 x 2 r f x

1 The table shows the wind chill factor for various wind speeds when the Fahrenheit temperature is 40 Wind Speed x 10 15 20 25 32 30 29 Wind chill degrees y 34 a Use your calculator to find the correlation coefficient r Round it to 3 decimal places 2 pts 30 35 28 28 b Find a linear regression model for the data using your calculator functions Write the equation showing numbers to 4 decimal places 4 pts c Use your model from part 4 to predict the wind chill for a wind speed of

12 You buy a sharing size package of 125 M Ms and 120 of them are red What is a 95 confidence interval for the true proportion of red M Ms in all sharing size packages 8 pts Round all figures to 3 decimal places

8 Determine if the variable is discrete or continuous 1 5 pts ea a No of ounces dispensed in a cup of coffee b No of televisions in a household

7 Identify the method of sampling simple random systematic stratified cluster convenience 4 pts a The country is divided into economic classes and a sample of 500 households from each economic class is selected b A sample of every 4th person leaving a theater is questioned about the movie

N Consider the following data set 120 170 157 172 183 162 156 84 195 169 158 171 a Obtain the five number summary for the given data 5 pts b Construct a box plot 5 pts 144 164 171 200

accompanying lavie are heights in of mothers and their first daughters The data pairs are from a journal kept by Francis Galton Use the listed paired sample data and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal Use a 0 05 significance level to test the claim that there is no difference in heights between mothers and their first daughters Mother 65 0 66 5 70 5 67 0 62 0 64 5 63 5 66 0 60 0 58 5 Daughter 67 0 68 5 61 7 67 0 64 5 65 2 63 7 66 0 61 0 66 5 Ho Hd in H Hd in Type integers or decimals Do not round Identify the P value

A high school guidance counselor has a pamphlet that says that 40 of all high school students go to a community college after graduation In a survey of 275 randomly selected high school seniors 123 replied that they planned to go to a community college in the fall Use a 95 confidence interval to test and see if the pamphlet needs updating Which of these facts would tell us that the pamphlet needs to be updated 000000 If an appropriate confidence interval contains the sample proportion If the sample proportion is the same as 40 If the sample proportion is different from 40 If an appropriate confidence interval does not contain the sample proportion If an appropriate confidence interval does not contain 40 If an appropriate confidence interval contains 40 In order to use a confidence interval to test whether the pamphlet needs to be updated what conditions must be checked Select all that apply 000000000 40 of all high school seniors needs to be at least n 275 The total population of all high school seniors needs to be at least n 275 100 40 of the sample n 1 p 165 students need to have said no they do not plan to go to a community college 110 students need to have said yes they plan to go to a community college 40 of the sample np The number of students in the sample who said they plan to go to community college n 123 students needs to be at least 10 The number of students in the sample who said they do not plan to go to community college n 1 p 152 students needs to be at least 10 40 of the sample np 110 students needs to be at least 10 100 40 of the sample n 1 p 165 students needs to be at least 10 The total population of all high school seniors needs to be more than 20n 5 500

According to the 2014 National Survey on Drug Use and Health 11 4 of adolescents in the United States had at least one major depressive episode MDE in the year prior to be being surveyed The percentage of MDE among adolescents was approximately three times higher for female adolescents 17 3 than for male adolescents 5 7 a Consider the American adolescent population as the sample space of interest Enter the three percents cited here using probability notation Enter your answers rounded to three decimal places P MDE P MDE female P MDE male b Is MDE independent of sex in the American adolescent population Select the best explanation None of the options are correct No MDE is not independent of sex in the American adolescent population Knowing the sex does not change the probability of MDE No MDE is not independent of sex in the American adolescent population Knowing the sex of the adolescent changes the probability of MDE Yes MDE is independent of sex in the American adolescent population since P MDF P male POMDE I mala

Polydactyly is a fairly common congenital abnormality in which a baby is born with one or more extra fingers or toes It is reported in about one child in every 500 A young obstetrician celebrates her first 100 deliveries Assuming that these 100 births are unrelated and independent what is the probability that the obstetrician has delivered no child with polydactyly Enter your answer rounded to four decimal places for example 0 1111 P X 0 What is the probability that she has delivered at least one child with polydactyly Enter your answer rounded to four decimal places P X 1

Birth certificates show that approximately 9 of all births in the United States are to teen mothers ages 15 to 19 24 to young adult mothers age 20 to 24 and the remaining 67 to adult mothers age 25 to 44 An extensive survey of live births examined pregnancy type defining an unintended pregnancy as one that was unwanted or mistimed by at least two years The survey found that only 23 of births to teen mothers are intended and 77 are unintended Among births to young adult women age 20 24 30 are intended and at ages 25 44 75 are intended The tree diagram of this information is shown Teen Young Adult or Adult P teen P unintended 0 09 0 24 P unintended teen P teen and unintended P teen unintended Intended or Unintended 0 0207 0 23 1 0 25 U 0 1675 a Use the information provided in the tree diagram to obtain the following probabiliti s Enter your answer as a percentage rounded to one decimal place 0 77 U 0 50 1 YA 0 67 A 0 751 P teen unintended OP unintended teen P unintended and teen 0 0693 0 1200 0 50 U 0 1200 0 5025 b The appropriate notation for the probability that an unintended birth was to a teen mother is

Manatees are an endangered species of herbivorous aquatic mammals found primarily in the rivers and estuaries of Florida As part of its conservation efforts the Florida Fish and Wildlife Commission records the cause of death for every recovered manatee carcass in its waters Of the 392 recorded manatee deaths in 2012 68 were perinatal and 81 were caused by collision with a watercraft a What is the probability that the death of a randomly selected manatee was due to collision with a watercraft Enter your answer rounded to four decimal places P collision b What is the probability that the death was not due to collision with a watercraft Enter your answer rounded to four decimal places P not collision c What is the probability that the cause of death was due to perinatal problems or collision with a watercraft What is the probability that it was due to some other cause Enter your answers rounded to four decimal places P perinatal or collision P other cause