Exam 23: Comparing Counts

Test the claim that the responses occur with percentages of 15%,20%,25%,25%,and 15% respectively.Use a 10% level of significance. Response A B C D E Frequency 12 15 16 18 19

In studying the occurrence of genetic characteristics,the following sample data were obtained.Are they uniformly distributed? Use a 10% level of significance. Characteristic A B C D E F Frequency 28 30 45 48 38 39

A candy company claims that its bags of mixed suckers are 20% strawberry,30% cherry,15% apple,10% lemon,and 25% grape.A bag was purchased,and the number of each type of flavour was recorded in the chart below. Flavor Count Strawberry 31 Cherry 15 Apple 17 Lemon 15 Grape 22

Describe a goodness-of-fit test.What assumptions are made when using a goodness-of-fit test?

Tests for adverse reactions to a new drug yielded the results given in the table.The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo)and the reaction (whether or not headaches were experienced). Drug Placebo Headaches 11 7 No headaches 73 91

When performing a chi-square goodness-of-fit test,why do large values of the test statistic suggest that the variable does not have the distribution stated in the null hypothesis? Refer to the formula for the test statistic in your explanation.

The two-way table summarizes data from the human resource department at a university: New Hires Tenure Adjunct Total Men 15 20 35 Women 15 20 35 Total 30 40 70 What is the probability (rounded to two decimal places)that a randomly selected new hire is a tenure-track woman?

A researcher performed a study to determine whether political party affiliations are different for different income brackets.She obtained the following sample data. Income Bracket party Low Middle High Total Conservative 101 130 97 328 NDP 78 113 146 337 Other 15 34 9 58 Total 194 277 252 723

A car insurance company performed a study to determine whether an association exists between age and the frequency of car accidents.They obtained the following sample data. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Age Group }$ Numberof accidentsin past3years Under 25 25-45 Over 45 Total 0 74 90 84 248 1 19 8 12 39 >1 7 2 4 13 Total 100 100 100 300 Does the data provide sufficient evidence to conclude that an association exists between age and frequency of car accidents? Use a 5% level of significance.

A researcher performed a study to determine whether political party affiliations are different for different income brackets.She obtained the following sample data. Income Bracket party Low Middle High Total Conservative 101 130 97 328 NDP 78 113 146 337 Other 15 34 9 58 Total 194 277 252 723

Among the eastern provinces in 2010,states,Nova Scotia has 40% of the total population,New Brunswick has 33%,Newfoundland has 21%,and Prince Edward Island has 6%.A market researcher selects a sample of 1000 subjects in 2011,with 450 in Nova Scotia,340 in New Brunswick,150 in Newfoundland,and 60 in Prince Edward Island.Does the distribution of the sample agree with the population distribution? Use a 1% level of significance.

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 54 times,recording the number of times each face appears. Face Count 1 9 2 15 3 6 4 12 5 6 6 6 How many degrees of freedom are there?

A publishing company performs sample surveys to obtain information on characteristics of book readers.A book reader is defined to be one who read one or more books in the six months prior to the survey; a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be one who did not read a book,newspaper,or magazine in the six months prior to the survey.The following data were obtained from a random sample of 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers,non-book readers,and non-readers are the same for each income bracket. Classification Book Non-book Non- Total household income reader reader reader Less than \ 15,000 173 267 55 495 \ 15,000 to \ 24,999 168 130 19 317 \ 25,000 to \ 39,999 160 144 9 313 \ 40,000 and over 213 88 3 304 Total 714 629 86 1429

A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges.She randomly selects 100 students from each college and records the number that smoke.The results are shown below. College A College B College C College D Smoke 17 26 11 34 Don't smoke 83 74 89 66 Are the proportions of students smoking the same for all four colleges? Use a 1% level of significance.

Test the claim that workplace accidents are distributed on workdays as follows: Monday 25%,Tuesday: 15%,Wednesday: 15%,Thursday: 15%,and Friday: 30%. In a study of 100 workplace accidents,24 occurred on a Monday,15 occurred on a Tuesday,17 occurred on a Wednesday,18 occurred on a Thursday,and 26 occurred on a Friday.Use a 10% level of significance.

A publishing company performs sample surveys to obtain information on characteristics of book readers.A book reader is defined to be one who read one or more books in the six months prior to the survey; a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be one who did not read a book,newspaper,or magazine in the six months prior to the survey.The following data were obtained from a random sample of 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers,non-book readers,and non-readers are the same for each income bracket. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Classification }$ Book reader Non-book reader Non- reader Total Less than \ 15,000 173 267 55 495 \ 15,000 to \ 24,999 168 130 19 317 \ 25,000 to \ 39,999 160 144 9 313 \ 40,000 and over 213 88 3 304 Total 714 629 86 1429 Household Income

Tests for adverse reactions to a new drug yielded the results given in the table.The data will be analyzed to determine if they provide sufficient evidence to conclude that an association exists between the treatment (drug or placebo)and the reaction (whether or not headaches were experienced). Drug Placebo Headaches 11 7 No headaches 73 91

A researcher records for each of 500 randomly selected towns,the number of churches in the town and the number of homicides in the town in the past ten years.The towns range in size from a population of 1000 to a population of 1,000,000.He then performs a chi-square test of independence for these two variables.Would you expect that he would find association between the two variables? If so,should he conclude that a causal relationship exists? Explain your thinking.

160 students who were majoring in either math or English were asked a test question,and the researcher recorded whether they answered the question correctly.The sample results are given below. Correct Incorrect Math 27 53 English 43 37 $x ^ { 2 }$ = 6.502; P-value = 0.011 Are the response and major independent? Use a 5% level of significance.

Describe the null hypothesis for the test of independence.List the assumptions for the χ2 test of independence.What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?