Statistics Questions

A 95 percent confidence interval for the true mean time spent preparing and recording a lecture is reported to be 75 to 95 minutes The point estimate for the true mean is Multiple Choice 90 minutes 80 minutes 85 minutes impossible to determine

The research department of a board game company surveyed some shoppers at a local mall The team asked shoppers how often they read the news among other questions Then the team played a memory card game with the shoppers They recorded how many cards each shopper remembered 0 times a week 1 2 times a week 1 3 cards 4 6 cards 7 5 2 3 What is the probability that a randomly selected shopper remembered 1 3 cards given that the shopper reads the news 0 times a week Simplify any fractions

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

4 18 Matching Pick the letter of the graph that goes with each numerical value listed below for the correlation Correlations 0 903 0 374 0 777 A Acreage 6 5 4 3 2 1 1 2 3 4 567 Full Bath

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

4 7 Sisters and Brothers The scatterplot shows the numbers of brothers and sisters for a large number of students Do you think the trend is somewhat positive or somewhat negative What does the direction positive or negative of the trend mean Does the direc tion make sense in this context Number of Brothers 9876543210

4 4 Shoe Size and GPA The figure shows a scatterplot of shoe size and GPA for some college students Does it show an increasing trend a decreasing trend or no trend Is there a strong relationship GPA 4 0 3 5 3 0 2 5 2 0 5 6 7 8 9 Shoe Size 10 11 12

Proceed as in Example 4 in Section 11 3 to find a particular solution xo t of equation 11 in Section 11 3 kx f t 11 m xp t dt k when m k 4 and the driving force f t is as given Assume that when f t is extended to the negative t axis in a periodic manner the resulting function is even f t 2mt 1 0 t 2m f t 2 f t 2 1 n 1

The Abco Company manufactures electrical assemblies The current process uses 10 workers and produces 200 units per hour You are considering changing the process with new assembly methods that increase output to 300 units per hour but will require 14 workers Workers are paid at a rate of 10 per hour Finished switches sell for 20 unit Using the information provided in Table below what is the multifactor productivity of the current process and the new process Based on your productivity calculations what decision should you make Should you go with the new process and why Show all your solution work and answers CURRENT PROCESS OUTPUT UNITS HOUR 200 NUMBER OF WORKERS 10 MATERIAL COST HOUR 120 NEW PROCESS 300 14 150

Consider the function C f x 1 0 x 1 1 20 0 x 1 0 Find the half range cosine expansion of the given function 1 200 f x n 1 Find the half range sine expansion of the given function f x 1 2 n 1

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

3 58 of students at a certain college are female 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

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

4 Assume that the finishing times in a New York City 10 kilometer road race are normally distributed with a mean of 63 minutes and a standard deviation of 8 minutes If one entrant in the race is randomly selected what is the probability that the entrant s finishing time is 66 minutes or more 6 pts Round to 4 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

5 To qualify for security officers training recruits are tested for stress tolerance The scores are normally distributed with a mean of 72 and a standard deviation of 9 If only the top 10 of recruits are selected find the cut off score for qualifying 6 pts Round to the nearest whole number

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

In 2012 the U S Food and Drug Administration approved the first over the counter HIV testing kit the OraQuick In Home HIV Test The sensitivity and specificity of a diagnostic test are determined experimentally The OraQuick test was approved based on a study that examined the test results of a sample of 4410 adults from a high risk population who did not yet know their HIV status Each person s actual HIV status was later confirmed via several other medical examinations The table contains the findings 105 true positives HIV and positive test 8 false negatives HIV and negative test 1 false positive no HIV and positive test 4296 true negatives no HIV and negative test Macmillan Learning What is the specificity P negative test no HIV of OraQuick This represents the fraction of all individuals with no HIV who received a negative test result Enter you answer rounded to four decimal places P negative test no HIV

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

Hemophilia refers to a group of rare hereditary disorders of blood coagulation Because the disorder is caused by defective genes on the X chromosome hemophilia affects primarily men According to the Centers for Disease Control and Prevention CDC the prevalence of hemophilia the number in the population with hemophilia at any given time among American males is 13 in 100 000 What does this mean The prevalence of 13 in 100 000 means that if you repeatedly sampled 100 000 males on average you would have 13 individuals with diagnosed with hemophilia per sample For one random sample of 100 000 males you hemophilia

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

A large governmental survey of dental care among children 2 to 17 years old found the distribution of times since the last visit to the dentist Time since last visit 6 months or less More than 6 months but no more than 1 year More than 1 year but no more than 2 years More than 2 years but no more than 5 years More than 5 years P more than 5 years Probability 0 57 P not within last 6 months 0 18 0 08 0 03 a What is the probability that a child has not seen a dentist in more than five years Enter your answer rounded to two decimal places b What is the probability that a randomly chosen child has not seen a dentist within the last six months Enter your answer rounded to two decimal places c What is the probability that the child has seen a dentist within the last year Enter your answer rounded to two decimal places

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

Determine whether to reject or fail to reject Ho at the level of significance of a a 0 08 and b a 0 05 Ho 138 H 138 and P 0 0646 MEERID a Do you reject or fail to reject Ho at the 0 08 level of significance A Reject Ho because P 0 08 OB Fail to reject Ho because P 0 08 OC Reject Ho because P 0 08 OD Fail to reject Ho because P 0 08 b Do you reject or fail to reject Ho at the 0 05 level of significance A Reject Ho because P 0 05 B Fail to reject Ho because P 0 05 OC Fail to reject Ho because P 0 05 D Reject H because P 0 05 tempts tempts tempts 68 49 C 41 of 36 of

A large study of German children of Caucasian descent found that 46 have brown hair and that 25 have freckles Nonetheless you cannot conclude that because 0 46 0 25 0 115 about 11 5 of German children of Caucasian descent are brown haired with freckles Why not O Having brown hair and having freckles are definitely independent events O Having brown hair and having freckles are not necessarily independent events Having brown hair and having freckles are not necessarily disjoint events Having brown hair and having freckles are definitely disjoint events

symbolic form More than 29 of Internet users pay bills online ess the full hypothesis Ho and the alternative hypothesis H in OC Ho p 0 29 H p 0 29 Which of the following is the hypothesis test to be conducted OA Ho p 0 29 H p 0 29 OE Ho p 0 29 H p 0 29 MICHICAS OB Ho p 0 29 H p 0 29 OD Ho p 0 29 H p 0 29 OF Ho p 0 29 H p 0 29 tempts tempts tempts

Find the A 3 The critical value s is are Round to two decimal places as needed Use a comma to separate answers as needed Draw a graph of the rejection region Choose the correct graph below XX s of a FO 3 talled 2 test with a 0 20 clade a graph with OB R 3 FO GEOR GS OC N 0 22 3 D 0 tempts tempts tempts

Use the given data to find the minimum sample size required to estimate a population proportion or percentage n Margin of error two percentage points confidence level 90 from a prior study p is estimated by the decimal equivalent of 42 Round up to the nearest integer

A researcher want to determine an interval estimate for the average weight of adult gorillas in pounds She wants to be 95 certain that she is within 5 7 of the true average From past studies it is known that the standard deviation of the weights of adult gorillas is 11 9 pounds What is the minimum sample size necessary to estimate the population mean Round your answer up to the next integer

An article reported that for a sample of 41 kitchens with gas cooking appliances monitored during a one week period the sample mean CO level ppm was 654 16 and the sample standard deviation was 166 25 a Calculate and interpret a 95 two sided confidence interval for true average CO level in the population of all homes from which the sample was selected Round your answers to two decimal places 601 69 X I 706 63 X ppm Interpret the resulting interval We are 95 confident that this interval contains the true population mean We are 95 confident that this interval does not contain the true population mean We are 95 confident that the true population mean lies below this interval We are 95 confident that the true population mean lies above this interval b Suppose the investigators had made a rough guess of 179 for the value of s before collecting data What sample size would be necessary to obtain an interval width of 40 ppm for a confidence level of 95 Round your answer up to the nearest whole number kitchens

A sample of ultimate tensile strength observations ksi was taken Use the accompanying descriptive statistics output from Minitab to calculate a 99 lower confidence bound for true average ultimat tensile strength and interpret the result Round your answer to two decimal places N 153 Mean 131 36 Median 131 37 TrMean 131 38 St Dev 4 59 SE Mean 0 37 Minimum 123 10 Maximum 148 70 We are 99 confident that the true average ultimate tensile strength is greater than 131 28 You may need to use the appropriate table in the Appendix of Tables to answer this question Q1 132 75 X ksi Q3 139 45

In a survey of 3484 adults aged 57 through 85 years it was found that 84 2 of them used at least one prescription medication a How many of the 3484 subjects used at least one prescription medication Round to the nearest integer as needed b Construct a 90 confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication p Round to one decimal place as needed tem tem temp temp tempt

Use the simplex method to find x 20 and x2 20 such that X 3x 221 X X 543 and such that z 12x 10x2 is maximized You MUST SHOW ALL STEPS REQUIRED of the simplex method Th includes the intital tableau and all row operations required to pivot The maximum is z when x and x

isted in the accompanying table are heights in of mothers and their first daughters The data pairs are from a journal kept by Francis Galton Use the isted 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 01 significance level to test the claim that there is no difference in heights between mothers and their first daughters M In this example g is the mean value of the differences d for the population of all pairs of data where each individual difference d is defined as the daughter s height minus the mother s height What are the null and alternative hypotheses for the hypothesis test Ho Ha H Pd in Type integers or decimals Do not round Identify the P value P value Round to three decimal places as needed What is the conclusion based on the hypothesis test in Mother 62 0 66 0 65 0 65 0 63 0 63 0 63 5 Daughter 68 0 66 0 64 5 62 0 65 0 63 0 63 5 tempts tempts tempts tempts tempts tempts

Find the standard score and the percentile for a data value 2 5 standard deviations above the mean O A z 2 5 Percentile 1 95 OB z 2 5 Percentile 0 62 C z 2 5 Percentile 99 38 z 0 25 Percentile 59 87 O D

A graduate student wanted to estimate the average time spent studying among graduate students at her school She randomly sampled graduate students from her school and obtained a 99 confidence interval of 17 3 22 5 hours week In the context of the problem which of the following interpretations is correct Choose the correct answer below OA Graduate students at this student s school study between 17 3 and 22 5 hours per week 99 of all weeks during the year OB There is a 99 chance that the average amount of time spent studying for all graduate students at this student s school is between 17 3 and 22 5 hours per week OC Approximately 99 of all random samples of graduate students from this school will give a mean number of hours studied per week between 17 3 and 22 5 OD We are 99 sure that the average amount of time spent studying among graduate students at this student s school is between 17 3 and 22 5 hours per week OE At this student s school 99 of all graduate students study between 17 3 and 22 5 hours per week on average te ter tem tem temp

A Use the given confidence interval limits to find the point estimate p and the margin of error E 0 768 0 944 6 0 E I

Salaries of 43 college graduates who took a statistics course in college have a mean x of 61 900 Assuming a standard deviation o of 10 395 construct a 95 confidence interval for estimating the population mean Click here to view at distribution table Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table 6A p Round to the nearest integer as needed te