Exam 23: Comparing Counts

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 in 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.Use a 1% level of significance. 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 $x ^ { 2 }$ = 114.534; P-value = 2.287 × $10 ^ { - 22 }$

Explain why a chi-square goodness-of-fit test is always right-tailed.

The sample data below was tested to determine whether car colour is related to the likelihood of being in an accident. Red Blue White Car has been in accident 49 11 30 Car has not been in accident 51 89 70 Test statistic: χ2 =34.38 P-value = 3.42 × $10 ^ { - 8 }$

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.Are the response and major are independent? Use a 5% level of significance. Correct Incorrect Math 27 53 English 43 37

Responses to a survey question are broken down according to gender and the sample results are given below.Are the response and gender are independent? Yes No Undecided Male 25 50 15 Female 20 30 10

A company says that each bag of their candy pieces contains 15% chocolate,27% butterscotch,10% caramel,7% peanut butter,and the rest toffee.You can buy a bag and separate the various kinds of candies.Upon weighing them,you find there are 30 grams of chocolate,48 grams of butterscotch,57 grams of caramel,63 grams of peanut butter and 90 grams of toffee.You wonder whether your bag is significantly different from what the company advertises.

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. AgeGroup Under25 25-45 Over45 Total Numberof 0 74 90 82 246 accidentsin 1 19 8 12 39 past3years >1 7 2 6 15 Total 100 100 100 300

A die is rolled 180 times and the following data are obtained.Is the die fair? Number Frequency 1 31 2 34 3 26 4 16 5 32 6 41

A researcher performed a study to determine whether an association exists between political party affiliation and income.She obtained the following sample data.Use a 1% level of significance. 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 $x ^ { 2 }$ = 27.831; P-value = 0.0000135

Research is conducted regarding the average age at retirement for four career groups.To test whether there is a relationship between age of retirement and career in these groups,700 employees,recently retired,are randomly selected.The resulting data are displayed in the contingency table below. age at retirement career 50-55 56-60 61-65 Over 65 Total Attorney 10 40 75 40 165 College Professor 5 30 80 60 175 Secretary 21 45 63 49 178 Store Clerk 18 44 70 50 182 Total 54 159 288 199 700 How many degrees of freedom are there for the chi-square test statistic?

In studying the occurrence of genetic characteristics,the following sample data were obtained.Do the characteristics occur with the same frequency? Use a 10% level of significance. Characteristic A B C D E F Frequency 28 30 45 48 38 39 χ2 = 8.263; P-value = 0.1423

A researcher wishes to test the effectiveness of a flu vaccination.Fifty randomly selected people are vaccinated,80 randomly selected people are vaccinated with a placebo,and 300 randomly selected people are not vaccinated.The number in each group who later caught the flu was recorded.The results are shown below. Vaccinated Placebo Control Caught the flu 7 14 19 Did not catch the flu 43 66 281

When performing a chi-square goodness-of-fit test,how are the expected frequencies obtained?

Tests for adverse reactions to a new drug yielded the results given in the table.Use a 10% level of significance. Drug Placebo Headaches 11 7 No headaches 73 91 $x ^ { 2 }$ = 1.798; P-value = 0.1799 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).

The following data were collected to determine whether or not the retirement age is the same for people in different professions. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Age at Retirement }$ 50-55 56-60 61-65 Over 65 Total Attorney 10 40 75 40 165 College Professor 5 30 80 60 175 Secretary 21 45 63 49 178 Store Clerk 18 44 70 50 182 Total 54 159 288 199 700 Career

Responses to a survey question are broken down according to employment status and the sample results are given below.Are the response and employment status independent? Use a 1% level of significance. Yes No Undecided Employed 40 15 5 Unemployed 10 25 10

A researcher performed a study to determine whether an association exists between sex and blood type.He obtained the following sample data. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Blood Type }$ Sex Total Female 162 138 40 20 360 Male 138 132 35 15 320 Total 300 270 75 35 680

A researcher performed a study to determine whether an association exists between political party affiliation and income.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 Does the data provide sufficient evidence to conclude that an association exists between political party affiliation and income? Use a 1% level of significance.

A researcher performed a study to determine whether an association exists between gender and blood type.He obtained the following sample data. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Blood Type }$ Sex Total Female 115 141 27 13 296 Male 86 91 26 9 212 Total 201 232 53 22 508 Does the data provide sufficient evidence to conclude that an association exists between gender and blood type? Use a 5% level of significance.

A researcher performed a study to determine whether an association exists between sex and blood type.He obtained the following sample data. Blood Type Sex Total Female 163 137 40 20 360 Male 137 133 35 15 320 Total 300 270 75 35 680