Exam 12: Inference on Categorical Data

A medical researcher is interested in determining if there is a relationship between adults over 50 who exercise regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Calculate the chi-square test statistic $\chi ^ { 2 }$ to test the claim that regular exercise and low, moderate, and high blood pressure are independent. Use $\alpha = 0.01$ . Blood Pressure Low Moderate High Reg. Exercise 35 62 25 No Reg. Exercise 21 65 28

Determine the expected counts for each outcome. $n=600$ 0.25 0.05 0.35 0.35 Expected Counts

Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6 . The data lists the number of wins for track hurdlers in the different starting positions. Test the claim that the probabilities of winning are the same in the different positions. Use α =0.05 . The results are based on 240 wins. Starting Position 1 2 3 4 5 6 32 44 36 33 45 50

The data below show the age and favorite type of reading of 779 randomly selected people. Test the claim thatage and preferred reading type are independent. Use α = 0.05. Age Current Events Mystery Science Fiction History 15-21 21 45 90 33 21-30 68 55 42 48 30-40 65 47 31 57 40-50 60 39 25 53

A teacher figures that final grades in the chemistry department are distributed as: A, 25 % ; B, 25 % ; C, 40 % ; D, 5 % ; F, 5 % . At the end of a randomly selected semester, the following number of grades were recorded. Find the critical value $x _ { 0 } ^ { 2 }$ to determine if the grade distribution for the department is different than expected. Use $\alpha$ =0.01 . Grade A B C D F Number 36 42 60 8 14

A researcher wants to determine if the number of minutes spent watching television per day is independent ofgender. A random sample of 315 adults was selected and the results are shown below. Is there enoughevidence to conclude that the number of minutes spent watching television per day is related to gender? Use α= 0.05. $\text { Gender }$$\quad$$\text { Minutes spent watching TV per day }$ 0-30 30-60 60-90 90 - over Male 25 35 75 45 Female 30 45 45 15

A random sample of 160 car purchases are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is $18 \%$ for the under 26 group, $39 \%$ for the $26 - 45$ group, $31 \%$ for the 45-65 group, and $12 \%$ for the group over 65 . Find the critical value $\chi \frac { 2 } { 0 }$ to test the claim that all ages have purchase rates proportional to their driving rates. Use $\alpha = 0.05$ . Age Under 26 26-45 46-65 Over 65 Purchases 66 39 25 30

In a chi-square test of homogeneity of proportions we test the claims that

A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Find the critical value $x _ { 0 } ^ { 2 }$ to test the claim that the probabilities show no preference. Use $\alpha$ =0.01 . Plan 1 2 3 4 5 Employees 30 55 32 18 65

The contingency table below shows the results of a random sample of 200 registered voters that was conductedto see whether their opinions on a bill are related to their party affiliation. Party Opinion Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the chi-square test statistic, , to test the claim of independence.

A random sample of 400 men and 400 women was randomly selected and asked whether they planned toattend a concert in the next month. The results are listed below. Perform a homogeneity of proportions test totest the claim that the proportion of men who plan to attend a concert in the next month is the same as theproportion of women who plan to attend a concert in the next month. Use α = 0.05. Men Women Plan to attend concert 230 255 Don't plan to attend concert 170 145

Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting positions. Find the critical value $x _ { 0 } ^ { 2 }$ to test the claim that the probabilities of winning are the same in the different positions. Use $\alpha$ =0.05 . The results are based on 240 wins. Starting Position 1 2 3 4 5 6 Number of Wins 45 36 32 33 44 50

Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6 . The data lists the number of wins for track hurdlers in the different starting positions. Calculate the chi-square test statistic $x ^ { 2 }$ to test the claim that the probabilities of winning are the same in the different positions. Use $\alpha$ =0.05 . The results are based on 240 wins. Starting Position 1 2 3 4 5 6 Number of Wins 33 50 44 32 36 45

A __________________ test is an inferential procedure used to determine whether a frequency distributionfollows a defined distribution.

A random sample of 160 car purchases are selected and categorized by age. The results are listed below. Theage distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26 -45 group, 31%for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic ?2 to test the claimthat all ages have purchase rates proportional to their driving rates. Use ? = 0.05. Age Under 26 26-45 46-65 Over 65 Purchases 66 39 25 30

A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Calculate the chi-square test statistic $x ^ { 2 }$ to test the claim that the probabilities show no preference. Use $\alpha$ =0.01 . Plan 1 2 3 4 5 Employees 65 32 18 55 30

The contingency table below shows the results of a random sample of 200 registered voters that was conductedto see whether their opinions on a bill are related to their party affiliation. Party Opinion Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Test the claim of independence.

A random sample of 160 car purchases are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18 % for the under 26 group, 39 % for the 26-45 group, 31 % for the 46-65 group, and 12 % for the group over 65 . Test the claim that all ages have purchase rates proportional to their driving rates. Use α=0.05 . Age Under 26 26-45 46-65 Over 65 Purchases 66 39 25 30

Test the null hypothesis of independence of the two classifications, A and B, of the 3 × 3 contingency tableshown below. Test using α = 0.10. 19 40 60 55 23 22 31 42 47

A researcher wants to determine if the number of minutes spent watching television per day is independent of gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi -square statistic $\chi ^ { 2 }$ to determine if there is enough evidence to conclude that the number of minutes spent watching television per day is related to gender. Use $\alpha = 0.05$ . $\text { Gender }$$\quad$$\text { Minutes spent watching TV per day }$ 0-30 30-60 60-90 90- over Male 25 35 75 45 Female 30 45 45 15