Exam 23: Comparing Counts

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 18 times,recording the number of times each face appears. Face Count 1 3 2 5 3 2 4 4 5 2 6 2 If the die is fair,how many times would you expect each face to show?

The table below shows the age and favorite type of music of 668 randomly selected people. Rock Pop Classical 15-25 50 85 73 25-35 68 91 60 35-45 90 74 77 Are age and preferred music type are associated? Use a 5% level of significance.

In order to test a claim about the effectiveness of a flu vaccine,150 people were vaccinated,180 people were vaccinated with a placebo,and 100 people were not vaccinated.The number in each group who later caught the flu was recorded.The researcher wishes to test the claim that the proportion of people who catch the flu is the same for all three groups.The results are shown below. Vaccinated Placebo Control Caught the flu 8 19 21 Did not catch the flu 142 161 79 Test statistic: χ2 = 14.965 P-value = 0.0005627

A researcher wishes to test the effectiveness of a flu vaccination.150 people are vaccinated,180 people are vaccinated with a placebo,and 100 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 8 19 21 Did not catch the flu 142 161 79 Are the proportions of people catching the flu the same in all three groups? Use a 1% level of significance.

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

The two-way table summarizes data from the human resource department at a university: New Hires Tenure Adjunct Total Men 23 18 41 Women 22 16 38 Total 45 34 79 What is the probability (rounded to three decimal places)that a female new hire is adjunct?

The following data were collected to determine whether or not the retirement age is the same for people in different professions. 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

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

Suspecting that a die may be unfair,you want to investigate.To check,you roll it 36 times,recording the number of times each face appears. Face Count 1 6 2 10 3 4 4 8 5 4 6 4 To see if these results are unusual,will you test goodness-of-fit,homogeneity,or independence?

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 CollegeD Smoke 17 26 11 34 Don't smoke 83 74 89 66 Test statistic: χ2 = 17.832 P-value = 0.0004763

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. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Age at Retirement }$ 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 Does the data provide sufficient evidence to conclude that an association exists between age of retirement and career? 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 data from a random sample. Blood Type Sex Total Female 115 141 27 13 296 Male 86 91 26 9 212 Total 201 232 53 22 508

The table below shows the age and favorite type of music of 668 randomly selected people.The data are to be used to compare the distribution of age for each music type.Use a 5% level of significance. Rock Pop Classical 15-25 50 85 73 25-35 68 91 60 35-45 90 74 77 $x ^ { 2 }$ = 12.954; P-value = 0.0115

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 Find $x ^ { 2 }$ .

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.He compiled the following data. Day Mon Tue Wed Thur Fri Absences 37 15 12 23 43 Test statistic: χ2 = 28.308 P-value = 0.0000108

What is the null hypothesis for the chi-square test of independence? What assumptions are required for this test?