Statistics Questions

Identify the parameters p and n in the following binomial distribution scenario A basketball player has a 0 511 probability of making a free throw and a 0 489 probability of missing If the player shoots 25 free throws we want know the probability that he makes no more than 10 of them Consider made free throws as successes in the binomial distribution Select the correct answer below O p 0 511 n 10 O p 0 511 n 25 O p 0 489 n 10 O p 0 489 n 25 111

Identify the option below that represents dependent events Select the correct answer below O rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw O rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two ro O drawing a 2 and drawing a 4 with replacement from a standard deck of cards rolling a 3 and then rolling a 4 with a standard die

Identify the option below that represents mutually exclusive events Select the correct answer below drawing a red card and then drawing a black card with replacement from a standard deck of cards O rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two ro rolling a sum greater than 10 from two rolls of a standard die and rolling a 3 for the first roll drawing a 7 and then drawing another 7 with replacement from a standard deck of cards

A primary election is being held for a city to elect a new mayor Of the candidates 8 are Republicans 3 are third party candidates and 9 are Democrats If an independent voter randomly selects a candidate for mayor what is the probability that the candidate is third party Give your answer as a fraction

While commuting a driver sets her smartphone to randomly play songs from a pre selected list Of the songs on the list 6 are rock 5 are hip hop and 3 are country What is the probability that the first song played is rock Give your answer as a fraction

A bag contains 7 RED beads 10 BLUE beads and 3 GREEN beads If a single bead is picked at random what is the probability that the bead is RED Select the correct answer below OOO 10 20 13 20 7 20 17 20 20 TrendACY MORE INSTR

A deck of cards contains RED cards numbered 1 2 3 4 5 6 BLUE cards numbered 1 2 3 4 5 and GREEN cards numbered 1 2 3 4 If a single card is picked at random what is the probability that the card has an ODD number Select the correct answer below 10 HEEFT HE 15 8 15 14 15 6 15 2 15 15

A spinner contains the numbers 1 through 50 What is the probability that the spinner will land on a number that is not a multiple of 13 Give your answer as a fraction Provide your answer below

A deck of cards contains RED cards numbered 1 2 and BLUE cards numbered 1 2 3 4 5 Let R be the event of drawing a red card B the event of drawing a blue card E the event of drawing an even numbered card and Oth event of drawing an odd card Drawing the Blue 2 is an example of which of the following events Select all correct answers Select all that apply E BORO

A deck of cards contains RED cards numbered 1 2 3 4 5 6 and BLUE cards numbered 1 2 3 4 5 Let R be the event of drawing a red card B be the event of drawing a blue card E be the event of drawing an even numbered card and O be the event of drawing an odd card Drawing the Blue 3 is an example of which of the following events Select all that apply OB

Question A deck of cards contains RED cards numbered 1 2 3 4 5 and BLUE cards numbered 1 2 Let R be the event of drawing a red card B the event of drawing a blue card E the event of drawing an even numbered card and Othe event of drawing an odd card Drawing the Red 1 is one outcome of which of the following events Select all correct answers Select all that apply

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

If P A 0 34 and P A or B 0 71 which of the following is false O P A given B 34 if A and B are mutually exclusive OP A an B 191 if A and B are independent O P B 561 if A and B are independent OP B 37 if A and B are mutually exclusive OP B Cannot be determined if A and B are neither mutually exclusive nor independe

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

A random sample of the price of gasoline from 30 gas stations in a region gives the statistics below Complete parts a through y 3 89 s 0 25 a Find a 95 confidence interval for the mean price of regular gasoline in that region 3 797 3 983 Round to three decimal places as needed b Find the 90 confidence interval for the mean Round to three decimal places as needed

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

Which statement about the S3 method is incorrect The t test is an example of the method The plot data frame is an example of the method O It belongs to generic O The S3 methods are R functions they can be called directly

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

We can set the class attribute of a base object to create an instance of an S3 class Which statement of follows about the class attribute is incorrect S3 has no formal definition of a class The class of an object can be a vector and the order of entries doesn t matter O You can determine the class of an S3 object with the class function You can change the class of an object to any nonexistent class name

Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables Use a significance level of 0 05 Internet Users Award Winners O A Award Winners 12 30 Internet Users 90 79 3 80 4 5 4 9 O OB Award Winners LV 12 04 30 56 3 3 2 Ho P H P Type integers or decimals Do not round The linear correlation coefficient is r 0 Round to three decimal places as needed Determine the null and alternative hypotheses The test statistic is t Round to two decimal places as needed A Internet Users The P value is Round to three decimal places as needed HM A 68 7 76 6 1 6 10 9 90 Ly O C Award Winners 12 04 30 38 3 0 1 e TITTH Internet Users 90 S Award Winners D 12T 30 O Internet Users 90 Because the P value of the linear correlation coefficient is the significance level there sufficient evidence to support the claim that there is a linear correlation between Internet users and scientific award winners M

The data show the chest size and weight of several bears Find the regression equation letting chest size be the independent x variable Then find the best predicted weight of a bear with a chest size of 39 inches Is the result close to the actual weig significance level of 0 05 44 213 41 41 55 51 42 D 206 176 309 300 178 Chest size inches Weight pounds Click the icon to view the critical values of the Pearson correlation coefficient r What is the regression equation y 210 89 7x Round to one decimal place as needed What is the best predicted weight of a bear with a chest size of 39 inches The best predicted weight for a bear with a chest size of 39 inches is Round to one decimal place as needed is the result close to the actual weight of 226 pounds OA This result is very close to the actual weight of the bear OB This result is not very close to the actual weight of the bear OC This result is exactly the same as the actual weight of the bear OD This result is close to the actual weight of the bear pounds Critical Values of the Pearson Correlation Coefficient r n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 n Critical Values of the Pearson Correlation Coefficient r a 0 05 0 01 0 950 0 878 0 811 0 754 0 707 0 666 0 632 0 602 0 576 0 553 0 532 0 514 0 497 0 482 0 468 0 456 0 444 0 396 0 361 0 335 0 312 0 294 0 279 0 254 0 236 0 220 0 207 0 196 a 0 05 0 990 0 959 0 917 0 875 0 834 0 798 0 765 0 735 0 708 0 684 0 661 0 641 0 623 0 606 0 590 0 575 0 561 0 505 0 463 0 430 0 402 0 378 0 361 0 330 0 305 0 286 0 269 0 256 x 0 01 NOTE To test H p 0 against H p 0 reject H if the absolute value of ris greater than the critical value in the table X

The accompanying table lists the ages of acting award winners matched by the years in which the awards were won Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to support a daim of linear correlation between the two variables Should we expect that there would be a correlation Use a significance level of a 0 01 Click the icon to view the ages of the award winners Construct a scatterplot Choose the correct graph below OA 20 20 70 Best Actress years Q EA The linear correlation coefficient is r Round to three decimal places as needed Determine the null and alternative hypotheses PV Ho P H P Type integers or decimals Do not round The test statistic is t Round to two decimal places as needed The P value is Round to three decimal places as needed Because the P value of the linear correlation coefficient is Should we expect that there would be a correlation OB Yes hacaure Best Actore and Rort Actrnes 70 204 20 70 Best Actress years OA No because Best Actors and Best Actresses are not typically the same age OB Ye Q G the significance level there O C 70 Best Actresses and Best Actors Print 20 correlated 20 70 Best Actress years Best Actress 29 29 30 61 33 33 43 28 66 23 42 42 51 D Best Actor 44 39 38 45 47 46 56 52 41 52 44 33 Q Done X OD 70 204 20 70 Best Actress years Q Q sufficient evidence to support the claim that there is a linear correlation between the ages of Best Actresses and Best Actors

Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables Should we expect that there would be a correlation Use a significance level of a 0 05 EEE Click the icon to view the ages of the award winners Construct a scatterplot Choose the correct graph below OA OB Best Actor year 20 LO THE 20 70 Best Actress years O 13 G Best Actor years 70 201 20 2 70 Best Actress years The linear correlation coefficient is r 0 334 Round to three decimal places as needed Determine the null and alternative hypotheses PLI Ho P H P Type integers or decimals Do not round O OC Best Actor years 70 20 20 PC 19 www 70 Best Actress years O D Best Actor yeam 70 20 20 70 Best Actress years O O C

Poker is a common game in which players are dealt five cards from a deck of cards It can be shown that there are 2 598 960 different possible poker hands The winning hands from highest to lowest are shown in the table below Find the requested F Use a calculator Show your answer to nine decimal places P straight Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3 744 hands Flush 5 108 hands Straight 10 200 hands Three of a kind 54 912 hands Two pair 123 552 hands One pair 1 098 240 hands 444 20 WARHO V iv in

A chemist has a 100 gram sample of a radioactive material They recorded the amount of radioactive material every week for 6 weeks The image below shows the Desmos output for an exponential regression model of the data collected by the chemist w a bt Log Mode STATISTICS R 0 9723 PARAMETERS O a 103 573 b 0 861358 Using the outnut above what weight does the model predict for week 7

For each of the following situations find the critical value s for z or t a Ho p 0 8 vs HA P 0 8 at a 0 01 b Ho p 0 2 vs HA p 0 2 at a 0 05 c Ho 40 vs HA 40 at 0 05 n 41 d Ho p 0 8 vs HA p 0 8 at a 0 01 n 335 e Ho p 50 vs HA 50 at a 0 05 n 1000 a The critical value s is are Use a comma to separate answers as needed Round to two decimal places as needed

Suppose the probability of an event E is 0 20 Consider the process to find the odds in favor of this event Identify the following P E P E What are the odds in favor of this event

8 Correlation and Regression Homework Part 1 of 2 K The accompanying table shows the percentage of employment in STEM science technology engineering and math occupations and mean annual wage in thousands of dollars for 16 industries The equation of the regression line is y 1 218x 45 906 Use these data to construct a 95 prediction interval for the mean annual wage in thousands of dollars when the percentage of employment in STEM occupations is 12 in the industry Interpret this interval Click the icon to view the mean annual wage data Construct a 95 prediction interval for the mean annual wage in thousands of dollars when the percentage of employment in STEM occupations is 12 in the industry 0 y 0 Round to three decimal places as needed