Statistics Questions

Which of the data sets represented by the following box and whisker plots has the smallest standard deviation A B C H H 04 1

Body mass index BMI is a medical screening tool that measures body fat in an individual based on height and weight T following data sets include the BMI measurements for random samples of 7 individuals Use the range rule of thumb to estimate the standard deviation then determine which sample has the least amount of variation Select the correct answer below Sample 1 25 8 39 2 32 2 18 7 22 7 28 8 25 4 Sample 2 24 5 33 3 31 7 45 9 23 4 28 2 25 8 Sample 3 30 8 19 2 29 9 25 6 28 8 31 0 27 3 Sample 4 31 8 23 9 29 1 52 6 23 6 31 1 20 6

You are curious to see how strong of a correlation there is between the average temperature in your area and the total amount of popsicles you sell monthly Assume the data below is from 2022 Total number of popsicles sold Avg temp for the month in degrees F Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 238 364 418 428 508 718 842 746 580 508 450 324 51 57 63 70 76 84 83 82 80 69 64 57 1 Using Microsoft Excel create a scatter plot with the data above Be sure to label your scatterplot Create a linear trendline line of best fit to go with your scatterplot Display the correlation coefficient r and the equation for the line of best fit on your scatter plot

I AB 6 AD 3 x K ZAB The sides of the 4 BC 5 CD 6 AD 3 quadrilateral inscribed in a circle are AB Find the cosine ZABC 3 19 2 6 10 10 4 BC 4 5 CD x no such quadrilateral 6 10 10 5 10

Distributions A and B below which of the following statements are true Select All correct Answers A Select All that Apply A HAS LArger Mean HAS LArger Mean The means of A and B are equal B A has the larger standard Deviation

LAHAS LArcer Mean 2 B HAS LArGer Mean 3 The means of A and B are equal B HAS the Larger Standard Deviation

VII The graph below shows the graphs of several normal distributions labeled A B and C on the same axis Determine which normal distribution has the largest mean Select the correct answer below B C A

Your answer is incorrect According to the records of a soft drink company the bottles for their one liter sized products contain an average mean of 1 015 liters of beverage with a standard deviation of 0 14 liters As part of routine quality assurance a sample of 60 bottles has been taken The sample mean amount of beverage in these 60 bottles was 0 99 liters Assuming the company s records are correct find the probability of observing a sample mean of 0 99 liters or less in a sample of 60 bottles t least four decimal places Round your answer to at least three decimal places

D Incorrect Your answer is incorrect The highway patrol s policy is to issue Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 58 miles The records show that exactly 5 of the speeds exceed this limit Find the standard deviation of the speeds of tickets for cars with speeds exceeding 80 cars travelling on California freeways Carry your intermediate computations to at least four decimal places Round your answer to at least one decimal place hour miles miles hour X C

I can calculate the profit or loss from a stock sale 6 lifelong How I Did Circle one I m still learning it Elean Schenandore purchased 300 shares of CY Energy stock online and paid a total of 8 484 95 She sold the stock at 39 94 per share and paid a 39 95 sales commission a What was the net amount of the sale b What was the profit or loss from th e 1 point Personal Finance B I got it

Suppose X N 10 0 5 and x 11 5 Find and interpret the z score of the standardized normal random variable Provide your answer below The z score when x 11 5 is The mean is This z score tells you that x 11 5 is standard deviations to the right of the mean

Rosetta averages 148 points per bowling game with a standard deviation of 14 points Suppose Rosetta s points per bowling game are normally distributed Let X the number of points per bowling game Then X N 148 14 If necessary round to three decimal places Provide your answer below Suppose Rosetta scores 110 points in the game on Thursday The z score when x 110 is This z score tells you that x 110 is standard deviations to the left of the mean The mean is

Question Ken is conducting a study to determine if there is a significant correlation between two different types of fish More specifically he wants to find out if higher numbers of catfish are associated with higher or lower numbers of guppies These are both categorical variables Which of the following tests could he use O Chi square O ANOVA H O Linear regression O Multiple regression

Let us play a game of tossing coins A total of three fair coins are tossed each time You receive one point for each head and two points for each tail For example you would receive four 4 points if a toss yields two heads and one tail Define the number of points you receive in each toss as X a Analytical analysis Determine the probability distribution function of X i e fx x and show the analytical results using either a bar chart or histogram b Experiments Toss the three coins 30 times and create a table to record the outcomes i e number of points and their associated number of occurrence Plot the experimental results using either a bar chart or histogram Horizontal axis value of x or outcome value vertical axis relative frequency of the occurrence or number of occurrence 30 c Discussions Compare the results in a and b and discuss

A r v X has moment generating function MGF given by Mx t e 2t 18t all real t Then Var X 36 9 02 18

A set of data is summarized by the stem and leaf plot below Stem Leaf Provide your answer below The value 20 appears 43 appears 2 00012347778899 3 0112233456677888 4 00001113446679 5 0000111222366889 time s in the data set The value 31 appears time s in the data set The value 58 appears time s in the data set time s in the data set The va

The following is a data set of the average weekly number of cups of coffee consumed by employees in an office Find the mean and median and determine if the mean or median is the better measure of central tendency 6 1 7 6 35 3 9 3 6 8 9 6 8 9 3 9 Select the correct answer below Mean 6 5 Median 8 O The median is the better measure of central tendency Mean 6 5 Median 8 O The mean is the better measure of central tendency Mean 8 Median 6 5 The median is the better measure of central tendency Mean 8 Median 6 5 O The mean is the better measure of central tendency

The values and relative frequencies for a set of data are shown below Complete the cumulative relative frequency table Provide your answer below Data Value Relative Frequency Cumulative Relative Frequency 1 2 3 0 21 0 18 0 34 027

A small startup company wishes to know how many hours per week that its employees spend commuting to and from work The number of hours for each employee are shown below Construct a frequency table for grouped data using four classes 6 5 10 15 13 3 12 3 20 10 3 12 10 13 15 8 5 7 20 3 Provide your answer below

In order to study the mean blood pressure of people in his town Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group Which type of sampling is used Select the correct answer below O Convenience sampling O Cluster sampling Stratified sampling O Systematic sampling

A researcher is interested in seeing if there is a relationship between the use of a particular software program and of the user The researcher conducts a survey of adults in which she categorizes the respondents into one of two categories either 18 35years old or 35 years and older Is the study described observational or experimental If it is an experiment what is the controlled factor Select the correct answer below O The study is an experiment The controlled factor is age of the respondent O The study is an experiment The controlled factor is the software program O The study is an observational study O The study is an experiment The controlled factor is the survey B

10 6 4 N 200 protein in ug mL 0 50 100 200 400 800 1000 400 600 Absorbance 1 2 5 4 1 5 4 7 2 8 5 8 6 800 1000 1200 a In what range of protein concentration does the assay give useful results 1 b Suppose you have a sample containing an unknown amount of protein and you determined the absorbance of the sample to be 6 2 Based on the standard curve what is the concentration of the protein in the unknown 1 c Suppose you have a sample that gives an absorbance of 9 2 what is the

Use a calculator with a key or a key to solve the following The exponential function f x 564 1 032 models the population of a country f x in millions x years afte 1974 Complete parts a e a Substitute 0 for x and without using a calculator find the country s population in 1974 The country s population in 1974 was million b Substitute 22 for x and use your calculator to find the country s population to the nearest million in the year 1996 as modeled by this function The country s population in 1996 was million c Find the country s population to the nearest million in the year 2018 as predicted by this function The country s population in 2018 will be million d Find the country s population to the nearest million in the year 2040 as predicted by this function The country s population in 2040 will be e What appears to be happening to the country s population every 22 years million OA It appears that the population is growing by a factor of 3 every 22 years OB It appears that the population is growing by a factor of 2 every 22 years Oc There does not appear to be a pattern OD It appears that the population is decreasing by a factor of every 22 years

We would like to use the fixed point method to find the root of the function f x e 2x is 2 and we set g x f x x What is the where 1 x 2 Suppose the initial value g x at the end of two iterations O 1 48 1 54 O 1 68 O 1 34

Suppose that f is a continuous function We observe f a f b 0 in the range of a b Which of the following is correct There is only one root There is an undeterminable number of roots There is no root There is at least one root

The function f x 7 59 In x 65 models the percentage of first year college men in a certain country expressing antifeminist views by agreeing with the statement x years after 1969 Complete parts a b Statement The activities of a married woman are best confined to the home and family Men Women Agreeing w Statement The function overestimates the actual percentage The function underestimates the actual percentage Opposition to Feminism among First Year College Students 1970 2004 70 65 6 60 50 40 30 20 10 33 3 By how much does the function value differ from the actual percentage 50 6 40 1 38 of first year college men expressed antifeminist views Round to the nearest tenth as needed Does this function overestimate or underestimate the percentage displayed on the graph 37 0 36 9 18 2 18 1 16 8 a Use the function to find the percentage of first year college men expressing antifeminist views in 2004 Does this function overestimate or underestimate the percentage displayed on the graph By how much Use the function to find the percentage of first year college men expressing antifeminist views in 2004 15 8 1970 1980 1990 2000 2004 1 1 Round to the nearest tenth as needed b Use the function to project the percentage of first year college men who will express antifeminist views in 2010 1 2

What is the formula used to calculate the value of at in the linear trend equation Ft k at btk while using double exponential smoothing O ataFt 1 alat 1 bt 1 O at B bt bt 1 1 B bt 1 O at B bt bt 1 1 y bt 1 O at aft 1 1 a at 1 bt 1

Suppose it is certain that an earthquake will occur someday What is the probability to the nearest percent that it will occur while you are at work Assume you are at work 9 hours per day 245 days p year Assume a 365 day year

The gas phase decomposition of phosphine at 120 C PH3 9 1 4 P 9 3 2 H g is first order in PHs with a rate constant of 0 0180 s If the initial concentration of PH is 0 0924 M the concentration of PH3 wi M after 109 s have passed

Suppose that f is a uniform joint probability distribution function on 0 x 7 0 y 4 What is the formula for f What is the probability that X Y Select the correct choice below and fill in the answer box within your choice OA f x y OB f x y 0 if 0 x 7 and 0 y 4 otherwise The probability that X Y is fraction

Researchers wanted to study if couples having children are married They surveyed a large group of people The data are shown in the contingency table below What is the relative risk of being married for those who have children Round your answer to two decimal places Married Not Married Total Children No Children Total 97 35 132 68 71 139 165 106 271

A group of college freshman are targeted with a voter registration advertisement Another group of freshman are not targeted The table below shows how many of these freshman registered to vote What is the odds ratio for freshman targeted with the advertisement registering to vote against freshman not targeted with the advertisement registering to vote Round to two decimal places Targeted with advertisement Not targeted with advertisement Total Registered to vote Did not register to vote 103 78 181 36 64 100 Total 139 142 281

tors are testing a new antidepressant A group of patients all with similar characteristics take part in the study me of the patients receive the new drug while others receive the traditional drug During the study a number o ents complain about insomnia The data are shown in the contingency table below What is the relative risk of omnia for those who receive the new drug Round to two decimal places Insomnia No insomnia New drug Traditional drug 36 88 Total 52 226 295 521 Total 278 331 609 l

K Complete the table shown to the right for the population growth model for a certain country The projected 2042 population is million Round to one decimal place as needed 2004 Population millions 79 1

The matrix A det 2 a a11 a21 38 2 87 382 34 2 87 15 12 15 a12 922 34 A 87 a 34 2 b 0 which is the system a 2 The eigenvalue with positive imaginary part is For eigenvalue 2 the eigenvector v has components a and b that satisfy 38 a 15 b 0 where h i a 38 15 i 87 34 0 has characteristic equation b 0 b 0 Choosing the first component of the eigenvector as a 1 for 2 the eigenvector is a i

Researchers wanted to study if having a long beak is related to flight in birds They surveyed a total of 34 birds The data are shown in the contingency table below What is the relative risk of having long beaks for those birds that fly Round your answer to two decimal places Provide your answer below Long beak Not a long beak Total Flies Does not fly Total 11 3 14 8 12 20 19 15 34

Researchers want to study whether or not a fear of flying is related to a fear of heights They surveyed a large group of people and asked them whether or not they had a fear of flying and whether or not they had a fear of heights The data are shown in the contingency table below What is the odds ratio for people afraid of heights being afraid of flying against people not afraid of heights being afraid of flying Round your answer to two decimal places Do not round until the final answer Afraid of flying Not afraid of flying Total Provide your answer below Afraid of heights Not afraid of heights Total 76 33 109 82 370 452 158 403 561

Several studies have found that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and or services online The data the accompanying table show the age of respondents and their answer to the question how many minutes do you browse online retailers per week Complete parts a through d Click the icon to view the data table OA 600 300 15 40 Age 65 OB Wien cons 600 5 The equal spread condition because the Normal probability plot 300 0 15 40 Age 65 Q O C Br Ti min wk 600 3004 0 15 40 Age b Do you think a linear model is appropriate Explain OA The scatterplot appears to have slight curvature at one end of the age distribution so a linear regression may not be complete OB The scatterplot shows a curved line so a linear regression is not appropriate unless the variables are transformed to make the C The scatterplot shows points in a tightly clustered single stream that form a straight line so a linear regression is definitely ap D The scatterplot does not show any discernable trend or pattern so a linear regression is definitely not appropriate c Find the equation of the regression line 65 Browsing Time Age Round the constant to one decimal place as needed Round the Age coefficient to three decimal places as needed d Check the residuals to see if the conditions for inference are met satisfied because the scatterplot of the residuals against the predicted values shows an approximately straight line This is also the case because a histogram of the residuals extreme outliers satisfied because the Normal probability plot Data Table Age 22 50 44 33 55 61 38 22 21 45 52 33 18 17 21 Browsing Time min wk 493 186 180 384 121 120 276 480 510 252 126 359 570 588 498 Print Done 0 unimodal and symmetric The

Given the contingency table below determine the marginal distribution of the toys shapes Round your answer s to the nearest whole number Select all that apply Select all that apply 47 Toys Round Square Total Black 3 5 8 White 7 2 9 Total 10 7 17

Fill in the following contingency table and find the number of students who both do not go to the beach AND do not go to the mountains Students go to the beach do not go to the beach Total Provide your answer below go to the mountains do not go to the mountains Total 32 54 27 32

A survey of 160 employed citizens was conducted and the results are shown in the table below Given that a randomly selected survey participant does not work in an office what is the probability that this person works on Saturday Provide your answer as a fraction Does not Work Saturday Works Saturday Total Provide your answer below Does not Work in an Office 21 5 26 Works in an Office 65 69 134 Total 86 74 160

Researchers wanted to study if wearing cotton clothes is related to depression They surveyed a large group of peopl he data are shown in the contingency table below What is the odds ratio for people wearing cotton clothes being epressed against people not wearing cotton clothes being depressed Round your answer to two decimal places Cotton Not cotton Total Depressed Not depressed 122 420 542 189 263 452 Total 311 683 994 E

A group of 130 students at a private university were asked if they are full time or part time and if they have gym memberships The results are shown in the table below Given that a randomly selected survey participant is part me what is the probability that this student has a gym membership No Gym Membership Gym Membership Total rovide your answer below Part time 13 5 18 Full time 59 53 112 Total 72 58 130

A database system assigns a 32 character ID to each record where each character is either a number from 0 to 9 or a letter from A to F Assume that each number or letter being selected is equally likely Find the probability that at least 20 characters in the ID are numbers Use Excel to find the probability Round your answer to three decimal places

Alex wants to test the reliability of lie detector tests or polygraph tests He performs a polygraph test on a random sample of 12 individuals If there is more than a 50 chance that the tests result in no false positives that is the tes does not result in a true statement being recorded as a lie Alex will conclude that the tests are reliable If the probability of a lie detector test resulting in a false positive is 5 5 what will Alex conclude Use Excel to find the probability rounding to three decimal places Select the correct answer below O Alex will conclude that the test is reliable since the probability of no false positives is less than 0 5 Alex will conclude that the test is not reliable since the probability of no false positives is greater than 0 5 O Alex will conclude that the test is not reliable since the probability of no false positives is less than 0 5 O Alex will conclude that the test is reliable since the probability of no false positives is greater than 0 5 41

At a certain fast food restaurant 77 5 of the customers order items from the value menu If 14 customers are randomly selected what is the probability that at least 9 customers ordered an item from the value menu Use Excel to find the probability Round your answer to three decimal places Provide your answer below

A roulette wheel has 38 slots numbered 1 to 36 and two green slots labeled 0 and 00 Jim a dealer at a roulette table tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands The ball has an equally likely chance of landing in each slot If Jim spins the ball around the wheel 25 times what is the probability that the ball lands in a green slot at most twice Use Excel to find the probability Round your answer to three decimal places

A basketball player has a 0 603 probability of making a free throw If the player shoots 28 free throws what is the probability that she makes no more than 20 of them Round your answer to 3 decimal places if necessary Provide your answer below

A softball pitcher has a 0 672 probability of throwing a strike for each pitch If the softball pitcher throws 15 pitches what is the probability that more than 9 of them are strikes Round your answer to three decimal places Provide your answer below P X 9

The probability of winning on an arcade game is 0 568 If you play the arcade game 22 times what is the probability of winning more than 15 times Round your answer to three decimal places Provide your answer below