Review of Part 7 Inference When Variables Are Related
Problem 1
Which test? For each of the following situations, state whether you'd use a chi-foursquare goodness-of-fit exam, a chi-square test of homogeneity, a chi-square exam of independence, or some other statistical test:
a) A brokerage house wants to see whether the type of account a customer has (Silver, Gilt, or Platinum) affects the type of trades that customer makes (in person, by phone, or on the Cyberspace). It collects a random sample of trades fabricated for its customers over the past twelvemonth and performs a test.
b) That brokerage firm besides wants to know if the type of account affects the size of the account (in dollars). It performs a test to see if the hateful size of the account is the same for the iii account types.
c) The academic research office at a large customs higher wants to run across whether the distribution of courses chosen (Humanities, Social Science, or Science) is unlike for its residential and nonresidential students. It assembles terminal semester'south information and performs a test.
Robin C.
Numerade Educator
Trouble two
Which test again? For each of the following situations, state whether you'd utilise a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of in- dependence, or some other statistical exam:
a) Is the quality of a car affected by what day it was congenital? A auto manufacturer examines a random sample of the warranty claims filed over the past ii years to test whether defects are randomly distributed across days of the piece of work calendar week.
b) A medical researcher wants to know if claret cholesterol level is related to center illness. She examines a database of x,000 patients, testing whether the cholesterol level (in milligrams) is related to whether or not a person has heart illness.
c) A pupil wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly called students and performs a examination.
Robin C.
Numerade Educator
Problem 3
Dice Subsequently getting trounced by your piddling brother in a children's game, you doubtable the die he gave you to gyre may exist unfair. To cheque, you lot scroll it 60 times, recording the number of times each face appears. Do these results bandage doubt on the die'southward fairness?
a) If the dice is fair, how many times would y'all expect each face up to testify?
b) To run into if these results are unusual, will you examination goodness-of-fit, homogeneity, or independence?
c) State your hypotheses.
d) Check the conditions.
e) How many degrees of freedom are there?
f) Find $x^{2}$
and the P-value.
yard) State your conclusion
Robin C.
Numerade Educator
Trouble 4
Chiliad&Thou'due south As noted in an earlier chapter, the Master-foods Company says that until very recently xanthous candies made up xx% of its milk chocolate 1000&M's, crimson another xx%, and orangish, blue, and green ten% each. The rest are brown. On his way home from work the day he was writing these exercises, one of the authors bought a bag of apparently K&1000's. He got 29 xanthous ones, 23 red, 12 orangish, fourteen blue, eight green, and 20 brownish. Is this sample consistent with the company's stated proportions? Test an appropriate hypothesis and state your conclusion.
a) If the M&M'southward are packaged in the stated proportions, how many of each color should the author have expected to go far his bag?
b) To encounter if his bag was unusual, should he test goodness-of-fit, homogeneity, or independence?
c) State the hypotheses.
d) Bank check the conditions.
e) How many degrees of freedom are there?
f) Find $\chi^{2}$ and the P-value.
yard) State a conclusion.
Robin C.
Numerade Educator
Problem 5
Human births If at that place is no seasonal effect on human births, nosotros would expect equal numbers of children to be born in each season (winter, spring, summer, and autumn). A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in wintertime, 35 in spring, 32 in summer, and 28 in fall. She wonders if the excess in the spring is an indication that births are not compatible throughout the year.
a) What is the expected number of births in each season if there is no "seasonal consequence" on births?
b) Compute the $\chi^{2}$ statistic.
c) How many degrees of freedom does the $\chi^{ii}$ statistic have?
d) Find the $\alpha=0.05$ disquisitional value for the $\chi^{2}$ distribution with the appropriate number of df.
e) Using the disquisitional value, what do you conclude nearly the naught hypothesis at $\alpha=0.05 ?$
Robin C.
Numerade Educator
Problem 6
Bank cards At a major credit carte bank, the percentages of people who historically apply for the Silver, Golden, and Platinum cards are lx%, thirty%, and 10%, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gilded, and 35 for Platinum. Is in that location prove to suggest that the percentages for this promotion may be different from the historical proportions?
a) What is the expected number of customers applying for each type of bill of fare in this sample if the historical proportions are still true?
b) Compute the $\chi^{2}$ statistic.
c) How many degrees of freedom does the $\chi^{2}$ statistic take?
d) Find the $\alpha=0.05$ critical value for the $\chi^{two}$ distribution with the appropriate number of df.
due east) Using the critical value, what do yous conclude nearly the null hypothesis at $\blastoff=0.05 ?$
Robin C.
Numerade Educator
Problem 7
Nuts A company says its premium mixture of nuts contains 10% Brazil nuts, 20% cashews, twenty% almonds, and 10% hazelnuts, and the residue are peanuts. You buy a large tin and separate the various kinds of nuts. Upon weighing them, you lot find at that place are 112 grams of Brazil nuts, 183 grams of cashews, 207 grams of almonds, 71 grams of hazelnuts, and 446 grams of peanuts. You wonder whether your mix is significantly different from what the visitor advertises.
a) Explain why the chi-foursquare goodness-of-fit test is not an advisable way to find out.
b) What might you do instead of weighing the nuts in order to use a $\chi^{2}$ exam?
Robin C.
Numerade Educator
Problem viii
Mileage A salesman who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his mileage for several weeks and discovers that he averages 122 miles on Mondays, 203 miles on Tuesdays, 176 miles on Wednesdays, 181 miles on Thursdays, and 108 miles on Fridays. He wonders if this evidence contradicts his belief in a uniform distribution of miles across the days of the week. Explicate why it is non appropriate to examination his hypothesis using the chi-square goodness-of-fit test.
Robin C.
Numerade Educator
Problem nine
NYPD and race Demography information for New York Urban center signal that 29.2% of the under-18 population is white, 28.2% black, 31.5% Latino, 9.i% Asian, and 2% other ethnicities. The New York Civil Liberties Union points out that, of 26,181 police officers, 64.8% are white, xiv.5% blackness, xix.1% Latino and one.4% Asian. Do the police officers reflect the ethnic composition of the metropolis'south youth? Test an appropriate hypothesis and state your decision.
Robin C.
Numerade Educator
Problem 10
Violence confronting women 2009 In its written report When Men Murder Women: An Analysis of 2009 Homicide Data, 2011, the Violence Policy Heart (www.vpc.org) reported that 1818 women were murdered by men in 2009. Of these victims, a weapon could exist identified for 1654 of them. Of those for whom a weapon could be identified, 861 were killed by guns, 364 past knives or other cutting instruments, 214 by other weapons, and 215 past personal attack (battery, strangulation, etc.). The FBI'south Compatible Crime Report says that, among all murders nationwide, the weapon utilize rates were every bit follows: guns 63.4%, knives 13.1%, other weapons 16.viii%, personal assail 6.seven%. Is there evidence that violence against women involves different weapons than other violent attacks in the United states?
Robin C.
Numerade Educator
Problem 11
Fruit flies Offspring of certain fruit flies may have yellowish or ebony bodies and normal wings or short wings. Genetic theory predicts that these traits will appear in the ratio nine:3:3:one (nine yellow, normal: 3 yellow, short: 3 ebony, normal: one ebony, short). A researcher checks 100 such flies and finds the distribution of the traits to be 59, 20, 11, and 10, respectively.
a) Are the results this researcher observed consistent with the theoretical distribution predicted by the genetic model?
b) If the researcher had examined 200 flies and counted exactly twice as many in each category—118, 40, 22, 20—what decision would he have reached?
c) Why is at that place a discrepancy between the ii conclusions?
Robin C.
Numerade Educator
Trouble 12
Pi Many people know the mathematical constant $\pi$ is approximately 3.14. But that's not exact. To exist more precise, here are 20 decimal places: 3.14159265358979323846. Still not verbal, though. In fact, the actual value is irrational, a decimal that goes on forever without whatsoever repeating blueprint. But notice that at that place are no 0's and just one 7 in the 20 decimal places above. Does that pattern persist, or do all the digits testify up with equal frequency? The table shows the number of times each digit appears in the outset million digits. Test the hypothesis that the digits 0 through ix are uniformly distributed in the decimal representation of $\pi$.
Robin C.
Numerade Educator
Problem 13
Hurricane frequencies The National Hurricane Center provides data that list the numbers of large (category three, four, or v) hurricanes that have struck the Usa, by decade since 1851 (www.nhc.noaa.gov/dcmi.shtml). The data are summarized beneath.
$$\begin{array}{|c|c|c|c|} \hline {\text { Decade }} & {\text { Count }} & {\text { Decade }} & {\text { Count }} \\ \hline 1851-1860 & {6} & {1931-1940} & {8} \\ {1861-1870} & {1} & {1941-1950} & {ten} \\ {1871-1880} & {7} & {1951-1960} & {ix} \\ {1881-1890} & {5} & {1961-1970} & {6}\\{1891-1900} & {8} & {1971-1980} & {4} \\ {1901-1910} & {4} & {1981-1990} & {4} \\ {1911-1920} & {7} & {1991-2000} & {five} \\ {1921-1930} & {5} & {2001-2010} & {vii} \\ \hline \cease{array}$$
Recently, there'due south been some concern that perchance the number of large hurricanes has been increasing. The natural null hypothesis would exist that the frequency of such hurricanes has remained abiding.
a) With 96 large hurricanes observed over the 16 periods, what are the expected value(s) for each cell?
b) What kind of chi-foursquare test would exist appropriate?
c) Country the null and culling hypotheses.
d) How many degrees of freedom are there?
e) The value of $\chi^{two}$ is $12.67 .$ What's the P-value?
f) State your decision.
Robin C.
Numerade Educator
Problem fourteen
Lottery numbers The fairness of the South African lottery was recently challenged by one of the country's political parties. The lottery publishes historical statistics at its Website (http://world wide web.nationallottery.co.za/lotto/ statistics.aspx). Here is a table of the number of times each of the 49 numbers has been drawn in the main lottery and as the "bonus ball" number equally of June 2007:
$$\begin{array}{|c|c|c|c|c|c|} \hline {\text { Number }} & {\text { Count }} & {\text { Bonus }} & {\text { Number }} & {\text { Count }} & {\text { Bonus }} \\ \hline 1 & {81} & {14} & {26} & {78} & {12} \\ {2} & {91} & {16} & {27} & {83} & {16} \\ {3} & {78} & {14} & {28} & {76} & {7} \\ {iv} & {77} & {12} & {29} & {76} & {12} \\ {5} & {67} & {xvi} & {xxx} & {99} & {16}\\ 6 & {87} & {12} & {31} & {78} & {ten} \\ {7} & {88} & {15} & {32} & {73} & {xv} \\ {8} & {90} & {sixteen} & {33} & {81} & {xiv} \\ {nine} & {lxxx} & {9} & {34} & {81} & {13} \\ {10} & {77} & {19} & {35} & {77} & {15}\\{11} & {84} & {12} & {36} & {73} & {8} \\ {12} & {68} & {14} & {37} & {64} & {17} \\ {13} & {79} & {9} & {38} & {seventy} & {11} \\ {14} & {90} & {12} & {39} & {67} & {fourteen} \\ {15} & {82} & {9} & {40} & {75} & {13}\\{16} & {103} & {fifteen} & {41} & {84} & {xi} \\ {17} & {78} & {14} & {42} & {79} & {8} \\ {18} & {85} & {14} & {43} & {74} & {14} \\ {nineteen} & {67} & {18} & {44} & {87} & {14} \\ {20} & {90} & {xiii} & {45} & {82} & {nineteen}\\{21} & {77} & {13} & {46} & {91} & {x} \\ {22} & {78} & {17} & {47} & {86} & {16} \\ {23} & {90} & {fourteen} & {48} & {88} & {21} \\ {24} & {80} & {8} & {49} & {76} & {13} \\ {25} & {65} & {11} \\ \hline\end{array}$$
Nosotros wonder if all the numbers are equally likely to exist the "bonus ball."
a) What kind of test should we perform?
b) In that location are 655 bonus brawl observations. What are the appropriate expected value(s) for the test?
c) State the null and alternative hypotheses.
d) How many degrees of freedom are there?
due east) The value of $\chi^{2}$ is $34.five .$ What's the P-value?
f) Land your conclusion.
Robin C.
Numerade Educator
Problem fifteen
Childbirth, part 1 There is some concern that if a woman has an epidural to reduce pain during childbirth, the drug can go into the baby's bloodstream, making the baby sleepier and less willing to breastfeed. In December 2006, the International Breastfeeding Journal published results of a study conducted at Sydney Academy. Researchers followed up on 1178 births, noting whether the mother had an epidural and whether the infant was still nursing later on 6 months. Hither are their results:
TABLE CAN'T COPY
a) What kind of test would exist appropriate?
b) Country the null and alternative hypotheses.
Robin C.
Numerade Educator
Problem 16
Does your md know? A survey8 of articles from the New England Journal of Medicine (NEJM) classi- fied them according to the primary statistics methods used. The articles recorded were all noneditorial articles appearing during the indicated years. Let's merely wait at whether these articles used statistics at all.
Table CAN'T COPY
Has in that location been a change in the employ of Statistics?
a) What kind of test would be appropriate?
b) State the null and alternative hypotheses.
Robin C.
Numerade Educator
Problem 17
Childbirth, part two In Exercise 15, the table shows results of a study investigating whether aftereffects of epidurals administered during childbirth might interfere with successful breastfeeding. We're planning to do a chi-square test.
a) How many degrees of freedom are in that location?
b) The smallest expected count will be in the epidural/ no breastfeeding jail cell. What is it?
c) Bank check the assumptions and conditions for inference.
Robin C.
Numerade Educator
Problem xviii
Does your doctor know? (role ii) The table in Exercise 16 shows whether NEJM medical articles during various fourth dimension periods included statistics or not. We're planning to practise a chi-square test.
a) How many degrees of liberty are there?
b) The smallest expected count will be in the 1989/No cell. What is it?
c) Check the assumptions and conditions for inference.
Robin C.
Numerade Educator
Problem xix
Childbirth, function 3 In Exercises fifteen and 17, we've begun to examine the possible impact of epidurals on successful breastfeeding.
a) Summate the component of chi-foursquare for the epidural/ no breastfeeding cell.
b) For this exam, $\chi^{2}=xiv.87 .$ What's the P-value?
c) State your conclusion.
Robin C.
Numerade Educator
Problem twenty
Does your doctor know? (part iii) In Exercises 16 and 18, we've begun to examine whether the utilise of statistics in NEJM medical articles has changed over time.
a) Calculate the component of chi-square for the 1989/ No cell.
b) For this test, $\chi^{2}=25.28 .$ What's the P-value?
c) Country your conclusion.
Robin C.
Numerade Educator
Problem 21
Childbirth, function 4 In Exercises 15, 17, and xix, we've tested a hypothesis near the impact of epidurals on successful breastfeeding. The table shows the test'southward residuals.
Tabular array Tin'T Copy
a) Show how the residue for the epidural/no breastfeeding prison cell was calculated.
b) What can you conclude from the standardized residuals?
Robin C.
Numerade Educator
Problem 22
Does your doctor know? (part four) In Exercises 16, 18, and 20, we've tested a hypothesis about whether the use of statistics in NEJM medical articles has changed over time. The table shows the examination'southward residuals.
Table Tin'T COPY
a) Show how the residual for the 1989/No cell was calculated.
b) What can you conclude from the patterns in the standardized residuals?
Robin C.
Numerade Educator
Problem 23
Childbirth, part five In Exercises 15, 17, 19, and 21, we've looked at a report examining epidurals every bit one cistron that might inhibit successful breastfeeding of newborn babies. Suppose a broader study included several additional issues, including whether the mother drank alcohol, whether this was a first child, and whether the parents occasionally supplemented breastfeeding with bottled formula. Why would it not be appropriate to utilize chi-square methods on the $2 \times 8$ table with aye/no columns for each potential gene?
Problem 24
Does your doctor know? (part 5) In Exercises xvi, 18, 20, and 22, we considered information on articles in the NEJM. The original study listed 23 different Statistics methods. (The listing read: t-tests, contingency tables, linear regression, \ldots. Why would it not be appropriate to use a chi-foursquare test on the $23 \times iii$ table with a row for each method?
Problem 25
Internet use poll A Pew Enquiry poll in April 2009 from a random sample of U.Southward. adults asked the questions "Did you use the Cyberspace yesterday?" and "Are yous White, Black, or Hispanic/Other?" Is the response to the question about the Cyberspace independent of race?
Tabular array CAN'T COPY
a) Under the null hypothesis, what are the expected values?
b) Compute the $\chi^{ii}$ statistic.
c) How many degrees of liberty does it take?
d) Find the P-value.
eastward) What practise you conclude?
Robin C.
Numerade Educator
Trouble 26
Internet use poll, II The same poll as in Exercise 25 also asked the questions "Did you use the Internet yesterday?" and "What is your educational level?" Is the response to the question about the internet contained of educational level?
Tabular array Tin can'T Copy
a) Nether the aught hypothesis, what are the expected values?
b) Compute the $\chi^{2}$ statistic.
c) How many degrees of freedom does it have?
d) Find the P-value.
e) What do you lot conclude?
Sheryl E.
Numerade Educator
Problem 27
Titanic Here is a table nosotros starting time saw in Chapter 2 showing who survived the sinking of the Titanic based on whether they were crew members, or passengers booked in first-,second-, or third-class staterooms:
TABLE Tin can'T COPY
a) If we draw an individual at random, what's the probability that we will draw a fellow member of the crew?
b) What'due south the probability of randomly selecting a 3rd-form rider who survived?
c) What'south the probability of a randomly selected passenger surviving, given that the passenger was a first-course passenger?
d) If someone's chances of surviving were the same regardless of their condition on the send, how many members of the crew would you expect to have lived?
e) Land the nil and alternative hypotheses.
f) Requite the degrees of freedom for the exam.
thou) The chi-square value for the tabular array is 187.8, and the respective P-value is barely greater than 0. State your conclusions almost the hypotheses.
Sheryl E.
Numerade Educator
Trouble 28
NYPD and sex discrimination The table below shows the rank attained by male person and female officers in the New York Urban center Police force Department (NYPD). Exercise these data summaries bespeak that men and women are equitably represented at all levels of the department?
TABLE CAN'T Re-create
a) What's the probability that a person selected at random from the NYPD is a female?
b) What's the probability that a person selected at random from the NYPD is a detective?
c) Assuming no bias in promotions, how many female detectives would yous await the NYPD to have?
d) To run into if there is evidence of differences in ranks attained by males and females, will you test goodness-of-fit, homogeneity, or independence?
e) Country the hypotheses.
f) Test the conditions.
g) How many degrees of liberty are there?
h) The chi-square value for the table is 290.ane and the P-value is less than 0.0001. Land your conclusion almost the hypotheses.
Sheryl E.
Numerade Educator
Trouble 29
Titanic again Examine and comment on this tabular array of the standardized residuals for the chi-square test yous looked at in Exercise 27.
Table CAN'T Re-create
Robin C.
Numerade Educator
Problem thirty
NYPD again Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 28.
Table Tin'T Copy
Robin C.
Numerade Educator
Problem 31
Cranberry juice It's common folk wisdom that drinking cranberry juice can help forestall urinary tract infections in women. In 2001 the British Medical Journal reported the results of a Finnish report in which three groups of l women were monitored for these infections over six months. One group drank cranberry juice daily, another group drank a lactobacillus drink, and the third drank neither of those beverages, serving as a command group. In the control group, 18 women developed at least 1 infection, compared to 20 of those who consumed the lactobacillus drink and only 8 of those who drank cranberry juice. Does this report provide supporting evidence for the value of cranberry juice in warding off urinary tract infections?
a) Is this a survey, a retrospective report, a prospective study, or an experiment? Explain.
b) Will you exam goodness-of-fit, homogeneity, or independence?
c) Land the hypotheses.
d) Test the weather.
due east) How many degrees of freedom are in that location?
f) Find $\chi^{2}$ and the P-value.
one thousand) State your determination.
h) If yous ended that the groups are not the aforementioned, analyze the differences using the standardized residuals of your calculations.
Sheryl E.
Numerade Educator
Trouble 32
Cars A random survey of autos parked in the educatee lot and the staff lot at a large university classified the brands past country of origin, as seen in the tabular array. Are there differences in the national origins of cars driven past students and staff?
TABLE CAN'T Copy
a) Is this a test of independence or homogeneity?
b) Write appropriate hypotheses.
c) Check the necessary assumptions and conditions.
d) Detect the P-value of your test.
e) Country your conclusion and analysis.
Robin C.
Numerade Educator
Problem 33
Montana A poll conducted by the University of Montana classified respondents by whether they were male or female person and political political party, as shown in the table. We wonder if there is evidence of an clan between being male or female and party amalgamation.
$$\begin{array}{|l|l|l|} \hline{} & {\text { Democrat}} & \text {Republican} & {\text {Independent }} \\ \hline {\text { Male person }} & \quad\quad{36} & \quad\quad{45} & \quad\quad{24} \\ {\text { Female }} & \quad\quad{48} & \quad\quad{33} & \quad\quad{16}\\ \hline \end{assortment}$$
a) Is this a examination of homogeneity or independence?
b) Write an appropriate hypothesis.
c) Are the conditions for inference satisfied?
d) Find the P-value for your test.
e) State a complete decision.
Robin C.
Numerade Educator
Problem 34
Fish diet Medical researchers followed 6272 Swedish men for xxx years to meet if there was any association between the amount of fish in their diet and prostate cancer. ("Fatty Fish Consumption and Risk of Prostate Cancer," Lancet, June 2001)
$$\begin{array}{|l|l|}\hline \text{} & {\text { Total }} & {\text {Prostate }} \\ {\text { Fish Consumption }} & \text {Subjects} & {\text { Cancers }} \\ \hline {\text { Never/Seldom }} & {124} & {fourteen} \\ {\text { Modest Office of Diet }} & {2621} & {201} \\ {\text { Moderate Part }} & {2978} & {209} \\ {\text { Large Role }} & {549} & {42}\\ \hline\terminate{assortment}$$
a) Is this a survey, a retrospective study, a prospective study, or an experiment? Explain.
b) Is this a examination of homogeneity or independence?
c) Do yous encounter show of an association between the corporeality of fish in a homo'southward diet and his risk of developing prostate cancer?
d) Does this study prove that eating fish does not forestall prostate cancer? Explain.
Robin C.
Numerade Educator
Problem 35
Montana revisited The poll described in Exercise 33 too investigated the respondents' party affiliations based on what area of the land they lived in. Test an appropriate hypothesis nearly this tabular array and country your conclusions.
$$\begin{array}{|l|l|l|}\hline \text {} & {\text { Democrat }} & {\text { Republican }} & {\text { Independent }} \\ \hline \text { West } & {39} & {17} & {12} \\ {\text { Northeast }} & {15} & {30} & {12} \\ {\text { Southeast }} & {30} & {31} & {xvi}\\ \hline\end{array}$$
Robin C.
Numerade Educator
Problem 36
Working parents In April 2009, Gallup published results from data nerveless from a large sample of adults in the 27 European Union member states. One of the questions asked was, "Which is the most practicable and realistic option for child care, taking into business relationship the need to earn a living?" The counts below are representative of the entire collection of responses.
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a) Is this a survey, a retrospective written report, a prospective study, or an experiment?
b) Will yous examination goodness-of-fit, homogeneity, or independence?
c) Based on these results, do you recall men and women have differing opinions when information technology comes to raising children?
Robin C.
Numerade Educator
Problem 37
Maryland lottery In the Maryland Selection-3 Lottery, three random digits are drawn each day. A fair game depends on every value (0 to nine) being equally likely to show up in all three positions. If not, someone who detects a pattern could have advantage of that. The tabular array shows how many times each of the digits was drawn during a recent 32-week period, and some of them—4 and 7, for instance—seem to come up up a lot. Could this just exist a outcome of randomness, or is there bear witness the digits aren't equally likely to occur?
$$\begin{array}{|c|c|}\hline {\text { Digit }} & {\text { Count }} \\ \hline 0 & {62} \\ {i} & {55} \\ {ii} & {66} \\ {3} & {64} \\ {iv} & {75} \\ {five} & {57} \\ six & {71} \\ {7} & {74} \\ {8} & {69} \\ {9} & {61}\\ \hline\stop{array}$$
Robin C.
Numerade Educator
Problem 38
Stock market Some investors believe that stock prices testify weekly patterns, challenge for instance that Fridays are more likely to exist "up" days. From the trading sessions since Oct 1, 1928 nosotros selected a random sample of 1000 days on which the Dow Jones Industrial Boilerplate (DJIA) showed a gain in stock prices. The table shows how many of these brutal on each day of the calendar week. Sure plenty, more of them are Fridays—and Tuesday looks similar a bad 24-hour interval to own stocks. Can this be explained as merely randomness, or is at that place evidence hither to help an investor?
Robin C.
Numerade Educator
Problem 39
Grades Two different professors teach an introductory Statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader.
TABLE Tin'T Copy
a) Will y'all test goodness-of-fit, homogeneity, or independence?
b) Write appropriate null hypotheses.
c) Find the expected counts for each cell, and explicate why the chi-foursquare procedures are not appropriate.
Robin C.
Numerade Educator
Trouble forty
Full moon Some people believe that a full moon elicits unusual behavior in people. The table shows the number of arrests made in a pocket-size boondocks during weeks of six full moons and vi other randomly selected weeks in the same twelvemonth. We wonder if there is show of a difference in the types of illegal activeness that accept place.
TABLE CAN'T Re-create
a) Will you test goodness-of-fit, homogeneity, or independence?
b) Write advisable null hypotheses.
c) Find the expected counts for each cell, and explicate why the chi-square procedures are not advisable.
Robin C.
Numerade Educator
Trouble 41
Grades again In some situations where the expected cell counts are too small, as in the case of the grades given by Professors Alpha and Beta in Exercise 39, we tin can complete an analysis anyway. We can often proceed after combining cells in some way that makes sense and likewise produces a tabular array in which the conditions are satisfied. Hither nosotros create a new table displaying the aforementioned data, but calling D'southward and F'south "Below C":
TABLE CAN'T COPY
a) Discover the expected counts for each cell in this new table, and explicate why a chi-square procedure is at present appropriate.
b) With this alter in the table, what has happened to the number of degrees of freedom?
c) Test your hypothesis about the ii professors, and land an appropriate decision.
Robin C.
Numerade Educator
Problem 42
Full moon, next phase In Exercise 40 you found that the expected jail cell counts failed to satisfy the conditions for inference.
a) Detect a sensible style to combine some cells that will make the expected counts acceptable.
b) Test a hypothesis about the full moon and state your conclusion.
Robin C.
Numerade Educator
Trouble 43
Racial steering A subtle form of racial discrimination in housing is "racial steering." Racial steering occurs when real estate agents show prospective buyers only homes in neighborhoods already dominated by that family'south race. This violates the Fair Housing Deed of 1968. According to an article in Chance magazine (Vol. 14, no. 2 [2001]), tenants at a large flat circuitous recently filed a lawsuit alleging racial steering. The circuitous is divided into two parts: Department A and Department B. The plaintiffs claimed that white potential renters were steered to Section A, while African-Americans were steered to Department B. The table describes the data that were presented in courtroom to prove the locations of recently rented apartments. Exercise you think at that place is bear witness of racial steering?
Tabular array Tin can'T COPY
Harsh K.
Numerade Educator
Problem 44
Titanic, redux Newspaper headlines at the time, and traditional wisdom in the succeeding decades, have held that women and children escaped the Titanic in greater proportions than men. Here's a summary of the relevant data. Practice you think that survival was independent of whether the person was male or female? Explicate.
Robin C.
Numerade Educator
Trouble 45
Steering revisited You could have checked the data in Practice 43 for evidence of racial steering using ii-proportion z procedures,
a) Notice the z-value for this approach, and show that when you square your z-value, you go the value of $\chi^{ii}$ you lot calculated in Practise $37 .$
b) Testify that the resulting P-values are the same.
Problem 46
Survival on the Titanic, one more than time In Exercise 44 you could take checked for a deviation in the chances of survival for men and women using two-proportion z procedures.
a) Find the z-value for this arroyo.
b) Show that the square of your calculated value of $z$ is the value of $\chi^{ii}$ you calculated in Exercise 44 .
c) Show that the resulting P-values are the same.
Robin C.
Numerade Educator
Problem 47
Pregnancies Most pregnancies upshot in live births, just some cease in miscarriages or stillbirths. A June 2001 National Vital Statistics Report examined those outcomes in the Us during 1997, broken down past the age of the mother. The table shows counts consistent with that written report. Is there evidence that the distribution of outcomes is non the aforementioned for these age groups?
TABLE Tin'T Copy
Robin C.
Numerade Educator
Problem 48
Education by age Use the survey results in the tabular array to investigate differences in teaching level attained among different age groups in the United states.
TABLE Tin'T COPY
Robin C.
Numerade Educator
whitworthglachind.blogspot.com
Source: https://www.numerade.com/books/chapter/inference-when-variables-are-related/
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