Exam 23: Comparing Counts

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.Are absences uniformly distributed over the week? Use a 1% level of significance. Day Mon Tue Wed Thur Fri Absences 37 15 12 23 43

The two-way table summarizes data from the human resource department at a university: New Hires Tenure Adjunct Total Men 22 20 42 Women 18 24 42 Total 40 44 84 What is the probability (rounded to three decimal places)that a male new hire is tenure track?

Test the claim that the proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote.300 men and 300 women were randomly selected and asked whether they planned to vote in the next election.The results are shown below.Use a 10% level of significance. Men Women Plan to vote 170 185 Do not plan to vote 130 115

You roll a die 48 times with the following results.Is the die fair? Number 1 2 3 4 5 6 Frequency 14 13 2 12 3 4

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. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Age Group }$ Number of accidents in past 3 years 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

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.Use a 5% level of significance. 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 $x ^ { 2 }$ = 9.13; P-value = 0.0579

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.Use a 5% level of significance. 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 $x ^ { 2 }$ = 20.77; P-value = 0.0137

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 90 times,recording the number of times each face appears. Face Count 1 15 2 25 3 10 4 20 5 10 6 10 State your hypotheses.

A study conducted for a woman's magazine indicates that the number of children desired by newly-married Canadian couples is distributed as follows. Number of children desired Percent 0 9% 1 17% 2 55% 3 11% Over 3 8% A random sample of 600 couples in Ontario resulted in the following data. Number of children desired Frequency 0 55 1 118 2 340 3 60 Over 3 27 Ontario couples is different from that of the Canadian population as a whole.Use a 5% level of significance.

A die is rolled 180 times and the following data are obtained. Number Frequency 1 31 2 34 3 26 4 16 5 32 6 41 A chi-square test was conducted to determine whether or not the die is loaded (i.e.,that the six numbers are not equally likely).Use a 5% level of significance. $x ^ { 2 }$ = 11.8; P-value = 0.03763

The two-way table summarizes data from the human resource department at a university: New Hires Tenure Adjunct Total Men 22 15 37 Women 20 19 39 Total 42 34 76 What is the probability (rounded to three decimal places)that a new hire is female?

The two-way table summarizes data from the human resource department at a university: New Hires Tenure Adjunct Total Men 20 23 43 Women 16 24 40 Total 36 47 83 What is the probability (rounded to three decimal places)that a tenure-track new hire is female?

The data will be analyzed to determine if they provide sufficient evidence to conclude that an association exists between car colour and the likelihood of being in an accident. Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30

In studying the responses to a multiple-choice test question,the following sample data were obtained.Are the responses uniformly distributed? Use a 10% level of significance. Response A B C D E Frequency 12 15 16 18 19

Tests for adverse reactions to a new drug yielded the results given in the table.Is the treatment (drug or placebo)independent of the reaction (whether or not headaches were experienced)? Use a 5% level of significance. Drug Placebo Headaches 11 7 No headaches 73 91

A die,suspected of being unfair,was rolled 50 times.The number of times each face appeared was recorded in the following table. Face Count 1 8 2 10 3 9 4 11 5 5 6 7

At a high school debate tournament,half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts.The results are given in the table below.Is the proportion of wins the same for teams wearing suits as for teams wearing jeans? Use a 10% level of significance. Win Loss Suit 22 28 T-shirt 28 22

The data will be analyzed to determine if they provide sufficient evidence to conclude that an association exists between car colour and the likelihood of being in an accident. Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30

The two-way table summarizes data from the human resource department at a university: New Hires Tenure Adjunct Total Men 17 25 42 Women 20 21 41 Total 37 46 83 What is the probability (rounded to two decimal places)of a randomly selected new hire being tenure track given that the new hire is a woman?

Use the sample data below to test whether car colour affects the likelihood of being in an accident.Use a 5% level of significance. Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30