Statistics Questions and Answers

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

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

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

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

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

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

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

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 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

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

2 Consider regression though the origin i e straight line regression with popula tion intercept known to be zero with Var e x xo The corresponding regression model is Y x e i 1 n Find an explicit expression for the weighted least squares estimate of

Chicken farming is a multi billion dollar industry and any methods that increase the growth rate of young chicks can reduce consumer costs while increasing company profits possibly by millions of dollars An experiment was conducted to measure and compare the effectiveness of various feed supplements on the growth rate of chickens Newly hatched chicks were randomly allocated into six groups and each group was given a different feed supplement Below are some summary statistics from this data set along with box plots showing the distribution of weights by feed type Weight in grams 400 350 300 250 200 150 100 HIH casein casein horsebean linseed meatmeal 277 31 65 20 Mean SD 323 88 64 53 12 161 00 38 93 10 218 85 52 14 12 11 346 33 HI horsebean linseed meatmeal soybean sunflower 52 43 n 14

Suppose you have ten observations with some fixed standard deviation How many standard errors do you need to add and subtract from the sample mean so that you obtain 95 confidence intervals 1 64 1 83 1 96 2 23 2 26

midterm 1 and N 85 o 4 5 for midterm 2 If a STOR 155 student scores in the top ten percent of students who took midterm 1 and the 75th percentile of midterm 2 and his final grade is midtermi midterm2 what is the student s final grade 2 90 18 O None of the above 90 19 93 22 86 81 Q18 4 Points Suppose X is a random variable from the discrete probability distribution below X P X x 0 25 What is the expectation of X 4 89 3 1 O None of the above 2 75 1 5 2 10 3 15

Air quality measurements were collected in a random sample of 25 country capitals in 2013 and then again in the same cities in 2014 We would like to use these data to compare average air quality between the two years Should we use a paired or non paired test A paired test should be used because for each city the temperature at the two time points will be equal O A non paired test should be used because for each city the temperature at the two time points are independent A paired test should be used because for each city the temperature at the two time points are not independent A paired test should be used because for each city the temperature at the two time points are independent A non paired test should be used because for each city the temperature at the two time points are not independent

Which of the following is true based on the summary statistics below Min 3 Q1 6 Median 9 Q3 12 Max 20 O There are no outliers O There is an outlier at the lower end of the distribution but not the upper end O There is one outlier at the upper and lower end of the distribution O Impossible to determine from the information given There is an outlier at the upper end of the distribution but not the lower end

The next presidential election is predicted to have a fifty fifty split in votes for the top democrat and top republican candidate How many people should be polled to obtain a margin of error of 03 at a 95 confidence level On 747 On 1849 On 544 On 1067 On 456

A car manufacturer has recently updated its assembly process with the aim of reducing the proportion of defective vehicles Before the process change the proportion of defective vehicles was 0 12 After the change a sample of 500 vehicles was tested and 48 were found to be defective The manufacturer wants to know if there is significant evidence at a 0 05 level that the proportion of defective vehicles has decreased What are the null and alternative hypotheses and which statistical test should be used H0 p 0 096 Ha p 0 096 O HO p 0 12 Ha p 0 12 None of the above This is a two sample test O HO p 0 096 Ha p 0 096 O HO p 0 12 Ha p 0 12

The National Center of Education Statistics conducted a survey of high school seniors collecting test data on reading writing and several other subjects Here we examine a simple random sample of 200 students from this survey We would like to know if there is a significant difference in the average scores of students in the reading and writing exam After performing a hypothesis test we calculated a pvalue of 374 Based on the results of this hypothesis test would you expect a confidence interval for the average difference between the reading and writing scores to include 0 Since we failed to reject HO we would not expect a confidence interval to include 0 Since we failed to reject H0 we would expect a confidence interval to include 0 Since we rejected H0 we would expect a confidence interval to include 0 None of the above Since we rejected H0 we would not expect a confidence interval to include 0

For questions 9 10 Suppose we are interested in predicting the temperature in Fahrenheit of the striped ground cricket from their chirps per second We take a simple random sample of 15 striped ground crickets Below are the R outputs for a linear regression model Coefficients Estimate Std Error t value Pr ltl Intercept 25 2323 10 0601 2 508 0 026183 chirps 0 6012 5 475 0 000107 Signif codes 0 0 001 0 01 0 05 0 1 1 Multiple R squared 0 6975 What is the value that belongs in the box representing the slope of our line 09 11 25 Cannot determine from the given information 3 29 35 33

A factory produces motorcycles of which 1 are defective Ten motorcycles are randomly selected from production What is the probability there are at least two defective motorcycles out of the ten selected O 45 01 2 99 8 O1 99 0 None of the above O1 10 01 99 O1 99 0 01 99

Which of the following is NOT a necessary condition that must be checked when performing a hypothesis test for a difference in two proportions Success failure condition O Independence between groups O A sample size of at least 30 Independence within groups O The sampling distribution of the sample proportions for both samples is approximately normal

Researchers are interested in studying the effects of a new diet program They collect data from participants Each participant s weight is recorded before and after the diet program The researchers want to determine if there is a significant change in the average weight of the participants after they undergo the diet program Which type of statistical test is most appropriate for this scenario O Two sample proportion test O One sample mean test Two sample mean test O One sample proportion test Paired tort

For problems 14 15 let X be from a binomial n 20 p distribution If the variance of X is 5 what are the possible values of p 0 5 O 25 None of the above 0 2 O 33

This question 1 point s possible A random sample of 740 births in New York State included 357 boys and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0 512 Complete parts a through c a In testing the common belief that the proportion of male babies is equal to 0 512 identify the values of p and p p p Round to three decimal places as needed b For random samples of size 740 what sample proportions of male births are at least as extreme as the sample proportion of within your choice 357 740 Select the correct choice below and fill in the answer box es Round to three decimal places as needed OA Those that are greater than or equal to OB Those that are less than or equal to and those that are greater than or equal to OC Those that are both greater than or equal to and less than or equal to OD Those that are less than or equal to There Submit quiz 357 c In using the method of randomization with 1000 resamples it is found that 134 of them have sample proportions that are at least as extreme as 740 Using a significance level of 0 05 what should be concluded about the claim that the proportion of male births is equal to 0 512 the claim that the proportion of male births is equal to 0 512 sufficient evidence to

Bernard ran an experiment to test optimum power and time settings for microwave popcom His goal was to deliver popcorn with fewer than 10 of the kernels left unpopped on average He determined that power 9 at 4 minutes was the best combination To be sure that the method was successful he popped 8 more bags of popcorn selected at random at this setting All were of high quality with the percentages of unpopped kernels shown below 7 6 9 2 13 3 10 8 11 8 8 4 9 1 6 2 Does this provide evidence that he met his goal of an average of fewer than 10 unpopped kernels Use 0 05 as the P value cutoff level O A Ho 10 HA 10 OC Ho 10 HA 10 O E Ho 10 HA 10 Calculate the test statistic 1 0 t Round to three decimal places as needed Calculate the P value P value Round to four decimal places as needed 012 OB Ho 10 HA 10 OD Ho p 10 HA 10 OF 10 HA 10

A credit card company tested the effectiveness of a promotional campaign by recently sending out offers to a random sample of 60 000 cardholders Of those 1491 registered for the promotion Even though this is nearly a 2 5 rate a staff member suspects that the success rate for the full campaign will be no different than the standard 2 rate that they are used to seeing in similar campaigns What do you predict Consider an event to be rare if its probability of occurring is less than 0 10 Complete parts a c below a What are the hypotheses Let p be the population proportion of cardholders who will register for the promotion Ho P 0 02 0 02 HA P Type integers or decimals Do not round b Are the assumptions and conditions for inference met The Randomization Condition can reasonably be assumed to be satisfied The 10 Condition can reasonably be assumed to be satisfied The Success Failure Condition is satisfied c Do you think the rate would change if they use this fundraising campaign Explain The test statistic for the test is Round to two decimal places as needed The P value is Round to three decimal places as needed Reject the null hypothesis There is sufficient evidence to conclude that the success rate for this promotional campaign will be different from the standard 2 rate that the company is

In the last quarter of 2007 a group of 64 mutual funds had a mean return of 5 3 with a standard deviation of 3 4 Consider the Normal model N 0 053 0 034 for the returns of these mutual funds a What value represents the 40th percentile of these returns b What value represents the 99th percentile c What s the IQR or interquartile range of the quarterly returns for this group of funds a The value that represents the 40th percentile is Round to two decimal places as needed b The value that represents the 99th percentile is Round to two decimal places as needed c The IQR is Round to two decimal places as needed

A random sample of 180 students was asked how many songs were in their digital music library and what fraction of them was legally purchased Overall they reported having a total of 114 565 songs of which 25 3 were legal A research group found that a 99 confidence interval for the fraction of songs in students digital music libraries that are legal is 25 0 25 6 The research group that conducted this survey wants to provide the music industry with definitive information but they believe that they could use a smaller sample next time If the group is willing to have twice as big a margin of error how many songs must be included A total of songs must be included Type a whole number

In a survey on downloading music a poll asked 711 Internet users if they ever downloaded music from an Internet site that was not authorized by a record company or not and 21 responded yes Construct a 90 confidence interval for the true proportion of Internet users who have downloaded music from an Internet site that was not authorized What is the confidence interval Select the correct choice below and if necessary fill in the answer boxes within your choice OA The 90 confidence interval is COLDS Round to one decimal place as needed Use ascending order OB The conditions for constructing a confidence interval are not satisfied

Idenury the null and alternative hypotheses to test each of the following situations Complete parts a through c a An article from a business journal looked at 1126 CEOs from global companies and found that 40 had MBAS Has the percentage changed Let p be the proportion of CEOs with an MBA Ho P Vs HA P Type integers or decimals Do not round b Recently 12 of cars of a certain model have needed costly transmission work after being driven between 60 000 and 80 000 miles The car manufacturer hopes that the redes transmission component has solved this problem Let p be the proportion of cars needing transmission repair Ho P vs HA P Type integers or decimals Do not round c A market researcher for a cola company decides to field test a new flavor soft drink planning to market it only if he is sure that over 53 of the people like the flavor Let p be the proportion of people who like the flavor Ho P vs HA P Type integers or decimals Do not round

H Pi P2 You obtain a sample from the first population with 118 successes and 363 failures You obtain a sample from the second population with 32 successes and 192 failures What is the test statistic for this sample Round to three decimal places test statistic What is the p value for this sample Round to four decimal places p value The p value is less than or equal to a greater than a This test statistic leads to a decision to reject the null fail to reject the null As such the final conclusion is that The sample data support the claim that the first population proportion is greater than the second population proportion port the claim that the first population proportion is

Matrix Products Consider the matrices 2 84 8 1 23 8 8 A B 5 8 6 6 Of the possible matrix products ABC ACB BAC BCA CAB CBA which make sense A ACB BAC CAB only B ACB BAC CBA only C ABC BCA CAB only D all of them E none of them 2 10 2 5 10 10 699 and C 7 7 10 3 28 59

Polymorphism and inheritance are two of the main reasons to use OOP As R is primarily a functional programming language what functions does the S3 OOP system implement polymorphism and inheritance O It implements polymorphism through NextMethod and inheritance through UseMethod O It implements polymorphism through UseMethod and inheritance through NextMethod O It implements polymorphism and inheritance through UseMethod It implements polymorphism and inheritance through NextMethod

Which of the following functions is not the example of a polymorphic function in sd summary plot

The job of an S3 generic is to perform method dispatch Which statement about generics in S3 is correct We need to name generic function using a special naming scheme The generics will first search the method for the default class The generic is similar to the interface in encapsulated OOP O The generic must call NextMethod