Statistics Questions

new In the twentieth century it was a common practice in Southern California for houses to be built with pools in the back however that practice may be changing possibly as a measure to help reduce climate change A recent study examined a random sample of 13 houses built in Southern California in the twentieth century and an independent random sample of 65 new houses built in Southern California The sample of twentieth century houses contained 73 houses with pools and the sample of new houses contained 28 houses with pools Based on this survey can we conclude at the 0 05 level of significance that the proportion p of all Southern California twentieth century house that were built with pools is greater than the proportion p of all new Southern California houses that were built with pools Perform a one tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below If necessary consult a list of formulas a State the null hypothesis Ho and the alternative hypothesis H H 0 H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places e Can we conclude that the proportion of Southern California twentieth century houses built with pools is greater than the proportion for new homes H x X 119 0 0 X O S 00 OSO P Q 010 A O O O

stion 3 You are being tasked to run the finances of the workshop your team is organizing The total number attendees is 45 with 9000 of fix setup cost 125 meal cost per head and 200 course material cost Attendees Meal per head Course Material per head 45 125 200

NK estion You are weing tasked to run the finances of the workshop your team is organizing The total number of attendees is 45 with 9000 of fix setup cost 125 meal cost per head Attendees Meal per head Decorations Course Material per head 45 125 9000 200 K M N O P Q

15 Write any 5 numbers with mode equals 0

13 Write any 5 numbers whose median is 1

12 Write any 5 numbers whose mean is 5

The following frequency table summarizes a set of data What is the five number summary Value Frequency 7 2 8 3 10 2 11 1 13 2 14 2 1 2 16 17

For a data set of chest sizes distance around chest in inches and weights pounds of six anesthetized bears that were measured the linear correlation coefficient is r 0 948 Use the table available below to find the critical values of r Based on a comparison of the linear correlation coefficient r and the critical values what do you conclude about a linear correlation Click the ic The critical value Type integers o Table of Critical Values of r Number of Pairs of Data n 4 5 6 7 8 9 10 11 12 Critical Value of r 0 950 0 878 0 811 0 754 0 707 0 666 0 632 0 602 0 576 X

Eternal Jane is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in the mean distance in thousands of km driven on them before they need to be replaced In the company s testing lab Jane tests a random sample of 13 Puma tires and a random sample of 15 Eternal tires These samples are chosen independently For each tire she logs the distance driven in thousands of km before the tire would need to be replaced These data are shown in the table Puma Eternal Send data to calculator V Distances in thousands of km 50 8 51 6 49 7 53 7 53 3 55 7 54 1 50 5 54 5 52 8 56 5 56 7 53 1 43 8 40 1 47 5 34 3 50 0 68 6 57 7 34 4 48 5 47 2 45 5 58 7 63 6 50 0 49 0 Send data to Excel Assume that the two populations of distances driven are approximately normally distributed Can Jane conclude at the 0 10 level of significance that there is a difference between the population mean of the distances in thousands of km driven on Puma tires before they need to be replaced and the population mean of the distances in thousands of km driven on Eternal tires before they need to be replaced Perform a two tailed test Then complete the parts below Carry your intermediate computations to three or more decimal places If necessary consult a list of formulas a State the null hypothesis Ho and the alternate hypothesis H Ho O H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places 0 d Find the p value Round to three or more decimal places e At the 0 10 level of significance can Jane conclude that there is a difference between the mean distance in thousands of km driven on Puma tires before they need to be replaced and the mean distance in thousands of km driven on Eternal tires before they need to be replaced OYes No H Xx 4 X O S OSO D S P 00 20 D

A sample of 26 offshore oll workers took part in a simulated escape exercise resulting in the accompanying data on time set 388 350 354 352 378 424 322 395 402 374 374 371 363 366 364 329 338 395 368 377 357 354 407 331 397 391 368 a Construct a stem and leaf display of the data Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values Stems Leaves 32 33 34 35 36 37 38 39 40 41 42 How does it suggest that the sample mean and median will compare The display is negatively skewed so the mean will be greater than the median The display is reasonably symmetric so the mean and median will be close The display is positively skewed so the median will be greater than the mean The display is negatively skewed so the median will be greater than the mean The display is positively skewed so the mean will be greater than the median b Calculate the values of the sample mean x and median 2 Hint Ex 9631 Round your answers to two decimal places B x sec 7 sec c By how much could the largest time currently 424 be increased without affecting the value of the sample median Enter if there is no limit to the amount By how much could this value be decreased without affecting the value of the sample median Enter If there is no limit to the amount d What are the values of x and when the observations are reexpressed in minutes Round your answers to two decimal places

population of heights of all mature eucalyptuses in the forest is approximately normally distributed An article in a conservation journal claims that the standard deviation of this population is 7 85 m You are a researcher who wants to test this claim with a random sample of 56 mature eucalyptuses from the forest Based on your sample follow the steps below to construct a 95 confidence interval for the population standard deviation of all mature eucalyptus heights in the forest Then state whether the confidence interval you construct contradicts the article s claim If necessary consult a list of formulas a Click on Take Sample to see the results from the random sample Take Sample Point estimate of the population variance Sample size 0 Left critical value Right critical value 0 To find the confidence interval for the population standard deviation first find the confidence interval for the population variance Compute Enter the values of the point estimate of the population variance the sample size the left critical value and the right critical value you need for your 95 confidence interval for the population variance Choose the correct critical values from the table of critical values provided When you are done select Compute Number of mature eucalyptuses 56 0 00 Sample mean Sample standard deviation 7 27 0 00 93 45 95 confidence interval for the population variance 2 00 95 confidence interval for the population standard deviation 4 00 5 00 Critical values Left Right b Based on your sample graph the 95 confidence interval for the population standard deviation of all mature eucalyptus heights in the forest 0 995 31 735 0 005 85 749 Enter the values for the lower and upper limits on the graph to show your confidence interval Round the values to two decimal places For the point enter the claim 7 85 from the article on your graph 6 00 2 X0 975 36 398 0 025 77 38 95 confidence interval for the population standard deviation Sample variance 0 950 38 958 X0 050 73 311 52 8529 O No the confidence interval does not contradict the claim The claimed standard deviation 7 85 is inside the 95 confidence interval O No the confidence interval does not contradict the claim The claimed standard deviation 7 85 is outside the 95 confidence interval Yes the confidence interval contradicts the claim The claimed standard deviation 7 85 is inside the 95 confidence interval O Yes the confidence interval contradicts the claim The claimed standard deviations is outside the 8 00 c Does the 95 confidence interval you constructed contradict the article s claim Choose the best answer from the choices below X S 5 10 00 10 00

weight Away a company that sells weight loss plans often advertises the effectiveness of its plans by highlighting the stories of a few clients who have lost extraordinary amounts of weight The following histogram gives information about more typical clients summarizing the weight loss in pounds over the past month for a sample of 50 clients Note that a negative value for weight loss represents a weight gain Relative frequency 1 0 8 0 6 0 4 0 2 0 3 0 0 2 0 1 0 0 00 10 10 0 1 Based on the histogram draw the ogive the cumulative relative frequency polygon for the Weight Away data Cumulative relative frequency 0 16 0 00 0 26 0 10 20 Weight loss in pounds 0 0 22 0 00 10 Weight 1 30 0 00 20 0 16 Ce 40 0 1 0 00 50 30 0 00 40 0 00 50 X S A

3 The weight of pennies currently being minted is about 2 5 grams more or less Is this a counting of a discrete variable please circle your answer YES NO

16 Write any 5 numbers with no mode 17 Calculate the mean the median the mode the range th variance and the standard deviation for the following sampl 2 3 5 3 2 3 4 3 5 1 2 3 4 Answer mean the modes are the range is standard deviation median variance

8 In 1980 the Hawaii State Senate held hearings when it was considering a law requiring that motorcyclists wear helmets Some motorcyclists testified that they had been in crashes in which helmets would not have been helpful Which important group was not able to testify Answer

18 Calculate the variance and standard deviation for the samples a n 40 Ex 380 Ex 100 b n 20 Ex 18 Ex 17 Answer s Answer s

19 Find the fraction or proportion of the data according to rule that is contained in the interval 2 2s Chebyshev s 2 2s

22 Give the percentage of measurements in a dataset that are above and below each of the following percentiles a 71st percentile Answer above is below is b 59th percentile below is C 2nd percentile below in Answer above is Answer above is

21 Using the relation of the range with standard deviation Range 4 give an estimate of s the sample standard deviation when the value of the range is 24 Answer

10 An economist collects income data by selecting and interviewing subjects now then going back in time education records to see if they had the wisdom to take a statistics course between the years 1980 and 2005 What type of study is this please circle your answer EXPERIMENTAL OBSERVATIONAL

9 Certain cruise ship passengers are given magnetic bracelets which they agree to wear in an attempt to eliminate or diminish the effects of motion sickness What type of study is this EXPERIMENTAL OBSERVATIONAL plongo cirola

11 The Coca Cola Company has 366 000 stockholders and a poll is conducted by randomly selecting 30 stockholders from each of the 50 states The number of shares held by each sampled stockholder is recorded Is this Cluster Sampling or Stratified Sampling CLUSTER SAMPLING STRATIFIED

4 In Big City there are 3258 walk buttons that pedestrians can press at traffic intersections and 511 of them do not work Is this a counting of a discrete variable YES NO please circle your answer

12 Write any 5 numbers whose mean is 5 13 Write any 5 numbers whose median is 1 14 Write any 5 numbers whose mean is 3 and whose median is 6 15 Write any 5 numbers with mode equals 0

1 Name a Variable corresponding to Discrete data i e counting 2 Name a Variable corresponding to Continuous data i e measuring

6 Salaries of women who are chief executive officers of corporations What type of data is this QUANTITATIVE QUALITATIV please circle your answer

5 In a survey of 1059 adults it is found that 39 of them have guns in their homes based on a 2004 Gallup poll What type of data is this QUALITATIVE QUANTITATIVE please circle your answer

What kind of data should the input file for a call to load contain Binary Data

To exclude row names from being written to the output of a cal to write table which of the following argument specifications are correct row names FALSE row names TRUE row names 1

What kind of data should the input file for a call to source contain OR code

Can read table read a file directly from the internet O Yes O No

What kind of file is normally created using dump O R O RData Rmd

What is the default value of the header argument in read table FALSE O TRUE O NA

What kind of file is normally created using ORData O R Rmd save

In a study 5 000 adults were surveyed and the number of siblings each had X was recorded The probability distribution is given below Find the mean and the standard deviation of the probability distribution using a TI 83 TI 83 Plus or TI 84 graphing calculator Round the mean and standard deviation to four decimal places X 0 1 2 3 4 LO 5 6 7 8 9 P x 0 2745 0 3401 0 1541 0 1293 0 0591 0 024 0 01 0 007 0 0011 0 0008

Suppose we have an algorithm that can detect whether a particular type of photograph features a turtle We seek to demonstrate that our algorightm can out perform the state of the art which has a correct detection rate of 0 7501 We have set our significance level to 0 05 Our hypothesis pair is OHO p 0 7501 HA p 0 7501 OHO p 0 7501 HA p 0 7501 OHO p 0 7501 HA p 0 7501 OHO p 0 7501 HA p 0 7501 OHO p 0 7501 HA p 0 7501 Considering our significance level and using the standard normal model our Critical Region for our test statistic z is closest to Ogreater than or equal to 3 09023 Ogreater than or equal to 1 64485 Ogreater than or equal to 2 57583 Ogreater than or equal to 2 05375 Ogreater than or equal to 2 32635 Suppose we randomly select 423 photographs and our observed sample statistic is p hat 0 85106 Using the standard normal model our observed test statistic z is closest to 04 795974 3 78557 0 3 851125 0 032778 01 427011 Our decision is OWe reject the null hypothesis and conclude our algorithm out performs the state of the art in terms of correct detection rate Owe fail to reject the null hypothesis and do not conclude our algorithm out performs the state of the art in terms of correct detection rate

Question 2 Suppose we have a new method of blowing crystal glass We seek to demonstrate that our new method has a lower rate of imperfections than our current method which has an imperfection rate of 0 240 We have set our significance level to 0 005 Our hypothesis pair is OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 Considering our significance level and using the standard normal model our Critical Region for our test statistic z is closest to less than or equal to 3 09023 Oless than or equal to 2 05375 less than or equal to 2 32635 Oless than or equal to 2 57583 Oless than or equal to 1 64485 Suppose employing our new method through a mechanism that mimics randomization we create 903 crystal glassworks and our observed sample statistic is p hat 0 24031 Using the standard normal model our observed test statistic z is closest to 00 021812 O 5 666164 O 2 081979 02 125603 O 7 069161 Our decision is Owe fail to reject the null hypothesis and do not conclude our new method out performs our current method in terms of rate of imperfections We reject the null hypothesis and conclude our new method out performs our current method in terms of rate of imperfections

Consider this statistical test hypothesis pair HO p 9 10 Ha p 1 3 This is Oa well formed hypothesis about a sample distribution shape Oa well formed hypothesis about a population parameter Oa well formed hypothesis about a sample statistic not a well formed hypothesis pair ONot enough information to answer this question Our research hypothesis conjectures that our population parameter is greater than 1 3 Ois not correctly specified Oconjectures that our sample statistic is not equal to 1 3 Oconjectures that our sample statistic is less than 1 3 Oconjectures that our population parameter is less than 1 3 Oconjectures that our sample statistic is greater than 1 3 conjectures that our population parameter is not equal to 1 3 ONone of these answers are correct

Consider this statistical test hypothesis pair HO p 2 3 Ha p 2 3 This is Onot a well formed hypothesis pair Oa well formed hypothesis about a sample statistic Oa well formed hypothesis about a sample distribution shape Oa well formed hypothesis about a population parameter ONot enough information to answer this question Our research hypothesis Ois not correctly specified Oconjectures that our sample statistic is less than 2 3 Oconjectures that our sample statistic is greater than 2 3 ONone of these answers are correct Oconjectures that our population parameter is greater than 2 3 Oconjectures that our sample statistic is not equal to 2 3 Oconjectures that our population parameter is not equal to 2 3 Oconjectures that our population parameter is less than 2 3

Consider this statistical test hypothesis pair HO p 1 10 Ha p 1 10 This is Oa well formed hypothesis about a sample statistic Oa well formed hypothesis about a sample distribution shape Oa well formed hypothesis about a population parameter Onot a well formed hypothesis pair ONot enough information to answer this question Our research hypothesis Oconjectures that our sample statistic is less than 1 10 Oconjectures that our sample statistic is not equal to 1 10 Oconjectures that our population parameter is greater than 1 10 Oconjectures that our population parameter is not equal to 1 10 Ois not correctly specified Oconjectures that our sample statistic is greater than 1 10 None of these answers are correct Oconjectures that our population parameter is less than 1 10

Consider this statistical test hypothesis pair HO p 1 3 Ha p 1 2 This is ONot enough information to answer this question Oa well formed hypothesis about a sample distribution shape Oa well formed hypothesis about a sample statistic Onot a well formed hypothesis pair Oa well formed hypothesis about a population parameter Our research hypothesis Oconjectures that our population parameter is not equal to 1 2 Oconjectures that our population parameter is less than 1 2 Ois not correctly specified ONone of these answers are correct Oconjectures that our sample statistic is not equal to 1 2 Oconjectures that our population parameter is greater than 1 2 Oconjectures that our sample statistic is greater than 1 2 Oconjectures that our sample statistic is less than 1 2

3 Create the relative frequency of row table then make an observation about the frequencies Total Activity Male Jog Fly Kites 100 Female 1 27 100 Total 100 11 272 TO Picnic 15 27

TER 7 17 Views on Capital Punishment In carrying out a study of views on capital punishment a student asked a question two ways 1 With persuasion My brother has been accused of murder and he is innocent If he is found guilty he might suffer capital punishment Now do you support or oppose capital punishment 2 Without persuasion Do you support or oppose capital punishment Here is a breakdown of her actual data Men For capital punishment Against capital punishment Women SURVEY SAMPLING AND INI For capital punishment Against capital punishment With persuasion 6 9 With persuasion 2 8 No persuasion 13 2 No persuasion 5 5 a What percentage of those persuaded against it support capital punishment b What percentage of those not persuaded against it support capital punishment c Compare the percentages in parts a and b Is this what you expected Explain 7 18 Views on Capital Punishment Use the data given in Exercise 7 17 Make the two given tables into one table by combining men for capital punishment into one group men opposing it into another women for it into one group and women opposing it into another Show your two way table The student who collected the data could have made the results misleading by trying persuasion more often on one gender than on the other but she did not do this She used persuasion on 10 of 20 women 50 and on 15 of 30 men 50 a What percentage of the men support capital punishment What per centage of the women support it b On the basis of these results if you were on trial for murder and did not want to suffer capital punishment would you want men or women on your jury

4 Create the relative frequency of total table then make an observation about the frequencies Fly Kites Picnic Activity Male 30 Female Total Jog M 1750 20 50 TO SOU 1 50224 5150 5 50 25 50 Total 23 50 7 7150 So so 2 100

8 40 Taxes Suppose a poll is taken that shows that 281 out of 500 randomly selected independent people believe the rich should pay more taxes than they do Test the hypothesis that a majority more than 50 believe the rich should pay more taxes than they do Use a significance level of 0 05

than one bultet hole 7 20 Targets Bias or Lack of Precision Again a If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 Jl ill amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math clas the class are three juniors and two seniors Using numbers 1 3 to represent juniors and 4 and 5 to represent seniors sample out replacement Draw a sample of two people four times on each of parts a b c and d and then fill in the following table a Use the first line reprinted here from the random number table select your sample of two The selections are underlined 02779 72645 86009 B ooooooooooo CL 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 0000 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error selecting any particular shape is 0 20 A card is selected randomly and a person is asked to guess which card has been chosen The graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some 7 30 Bias Assuming that the true proportion of success for the trials shown in the graph for Exercise 7 27 is 0 2 explain whether any of the graphs shows bias 7 31 Fair Coin One of the graphs shows the proportion of heads SECTION EXERCISES CHAPTER 7 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 32699 Report the percentage of seniors in the sample Count the numb 4 s and 5 s and divide by the sample size 2 b Use the next line to select your sample of two 31867 85872 91430 45554 Report the percentage of seniors in the sample c Use the next line to select your sample of two 75298 75250 34546 07033 Report the percentage of seniors in the sample d Use the last line to select your sample of two 09541 80623 09084 98948 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples Repetition 1 from part a 2 from part b 3 4 p Population Proportion of Seniors 2 5 0 4 p Sample Proportion of Seniors 1 2 0 5 Error p 0 5 0 4 7 34 Simulation From a very large essentially infinite popul of which half are men and half are women you take a random s

is studying the sell image okers as me Dy psychologist the self image SI score from a personality inventory She would like to examine the mean SI score for the population of all smokers Previously published studies have indicated that the mean SI score for the population of all smokers is 80 and that the standard deviation is 12 but the psychologist has good reason to believe that the value for the mean has changed She plans to perform a statistical test She takes a random sample of SI scores for smokers and computes the sample mean to be 90 Based on this information complete the parts below a What are the null hypothesis and the alternative hypothesis II that should be used for the test Ho O H 0 b Suppose that the psychologist decides not to reject the null hypothesis What sort of error might she be making Choose one c Suppose the true mean SI score for all smokers is 80 Fill in the blanks to describe a Type I error A Type I error would be Choose one Choose one Choose one the hypothesis that u is Choose one when in fact is H 0 0 X XI OSO 0 0 4

7 17 Views on Capital Punishment In carrying out a study of views on capital punishment a student asked a question two ways 1 With persuasion My brother has been accused of murder and he is innocent If he is found guilty he might suffer capital punishment Now do you support or oppose capital punishment 2 Without persuasion Do you support or oppose capital punishment Here is a breakdown of her actual data Men For capital punishment Against capital punishment Women For capital punishment Against capital punishment With persuasion 6 9 With persuasion 2 8 No persuasion 13 2 No persuasion 5 5 a What percentage of those persuaded against it support capital punishment b What percentage of those not persuaded against it support capital punishment c Compare the percentages in parts a and b Is this what you expected

B 0 g 8 35 Gun Control Historically the percentage of U S residents who support stricter gun control laws has been 52 A recent Gallup Poll of 1011 people showed 495 in favor of stricter gun control laws Assume the poll was given to a random sample of people Test the claim that the proportion of those favoring stricter gun control has changed Perform a hypothesis test using a significance level of 0 05 See page 405 for guidance Choose one of the following conclusions i The percentage is not significantly different from 52 A significant difference is one for which the p value is less than or equal to 0 050 ii The percentage is significantly different from 52

A researcher studying stress is interested in the blood pressure measurements of chief executive officers CEOs of major corporations He has good reason to believe that the mean systolic blood pressure of CEOs of major corporations is more than 134 mm Hg which is the value reported in a possibly outdated journal article He plans to perform a statistical test He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 142 mm Hg and the standard deviation of the sample to be 18 mm Hg Based on this information complete the parts below a What are the null hypothesis H and the alternative hypothesis H that should be used for the test H D H 0 b Suppose that the researcher decides not to reject the null hypothesis What sort of error might he be making Choose one c Suppose the true mean systolic blood pressure of CEOs of major corporations is 146 mm Hg Fill in the blanks to describe a Type II error A Type II error would be Choose one Choose one Choose one V Choose one the hypothesis that u is when in fact is 0 0 X X OSO 9 0 020 0 0 0 S