Chapter 11 practice test Provide an appropriate response. 1) The two-way table summarizes data from a survey at a small liberal arts college: New Hires Tenure Adjunct Total Men Women Total
19 25 44
25 17 42
1)
44 42 86
What is the probability (rounded to two decimal places) that a randomly selected new hire is a tenure-track woman? A) 0.29 B) 0.20 C) 0.25 D) 0.60 E) 0.49
2) The two-way table summarizes data from a survey at a small liberal arts college: New Hires Tenure Adjunct Total Men Women Total
22 19 41
20 25 45
2)
42 44 86
What is the probability (rounded to three decimal places) that a tenure-track new hire is female? A) 0.463 B) 0.221 C) 0.477 D) 0.556 E) 0.432
Group the bivariate data into a contingency table. 3) The table below provides data on sex, political party affiliation, and income bracket for a sample of people questioned during a poll. Group the bivariate data for the two variables "sex" and "income bracket" into a contingency table. Sex M F F M F M F M M F M F F M M F M F M F M M
Political Party Income Bracket Rep Dem Dem Dem Other Rep Rep Rep Dem Rep Dem Rep Dem Dem Rep Dem Rep Other Other Dem Dem Rep
High Middle Middle Low Middle Low High High High Low High Middle Middle Middle Low High Low High Middle Low Middle Low
1
3)
F
Dem
Middle
A)
B)
C)
D)
E) None of the above. Provide an appropriate response. 4) During a poll, 146 people were randomly selected and asked their political party affiliation. The contingency table below shows the results cross classified by political party affiliation and sex.
Find the conditional distribution of political party affiliation for women. A) Democrats: 32.4%; Republicans: 37.8%; Others: 29.7% B) Democrats: 47.8%; Republicans: 44.0%; Others: 56.0.% C) Democrats: 16.4%; Republicans: 19.2%; Others: 15.1% D) Democrats: 31.5%; Republicans: 34.2%; Others: 34.2% E) Democrats: 52.2%; Republicans: 56%; Others: 44%
2
4)
Use contingency table to estimate expected cell count. 5) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Assuming the row and column classification are independent, find an estimate for the expected cell count of row 2, column 2. Round your answer to tenths. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 A) 24 B) 22.8 C) 22.2
D) 27.6
E) 46.92
Use chi-square table. 6) Use the appropriate table to find the following chi-square value: 2 = 0.025 for df = 2. A) 9.35 B) 7.38 C) 5.99 D) 2.77 E) 5.02 7) Use the appropriate table to find the following probability: P( 2 13.28) for df = 4. A) 0.005 B) 0.010 C) 0.100 D) 0.990
5)
E) 0.02
Use the contingency table. 8) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Use = 0.05.
6)
7)
8)
Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the rejection region to test the claim of independence. A) 2 > 16.92 B) 2 > 9.49 C) 2 > 7.81
D) 2 > 7.78
E) 2 > 11.14
9) The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the chi-square test statistic, 2 , to test the claim of independence. A) 9.483 B) 11.765 C) 4.41 D) 8.030
3
E) 7.662
9)
Select the most appropriate answer. 10) The chi-squared test statistic for testing the independence of two categorical variables is A) all cells
B) all cells
C) all cells
D)
10)
(observed cell count - expected cell count) observed cell count (observed cell count - expected cell count) expected cell count (observed cell count - expected cell count)2 expected cell count (observed cell count - expected cell count)2 observed cell count
all cells E) none of the above.
Provide an appropriate response. 11) In a 2 test of independence, the null hypothesis is that A) there is an association. B) the random variables are dependent. C) each sample has equal frequency. D) there is not an association. E) each element of each set has the same probablity of occurrences. 12) As the number of degrees of freedom increases, the 2 distribution A) becomes more symmetric. B) becomes less symmetric. C) becomes exponential. D) becomes less robust. E) does not change shape as the degrees of freedom change. Select the most appropriate answer. 13) Whenever a statistic has a standard normal distribution, the square of that statistic has a chi-squared distribution with A) df = (r - 1) × (c - 1). B) df = (n -1)2 . C) df = n -1. D) df = n -2. E) df = 1. 14) The minimum possible value of the chi-squared test statistic, X2 = 0, would occur if the observed count is A) less than the expected count in each cell. B) equal to the expected count in each cell. C) more than the expected count in each cell. D) less than the expected count as often as it is more than the expected count. E) .equal to the expected count overall.
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11)
12)
13)
14)
15) The degrees of freedom in a chi-squared test of independence of two categorical variables which produce a 3 × 8 contingency table are A) 20. B) 14. C) 24. D) 23. E) 22. State the null hypothesis to test for independence. 16) Responses to a survey question are broken down according to employment status and the sample results are given below. At the 0.10 significance level, test the claim that response and employment status are independent. Yes No Undecided Employed 30 15 5 Unemployed 20 25 10 A) H0 : Employment status and response are independent.
15)
16)
B) Ha: Employment status and response are dependent. C) Ha: Employment status and response are independent. D) H0 : Employment status and response are dependent.
17) 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 Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent. A) H0 : Age and preferred music type are independent.
17)
B) H0 : Age and preferred music type are dependent.
C) Ha: Age and preferred music type are dependent. D) Ha: Age and preferred music type are independent. Calculate 2 from contingency table. 18) Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05 significance level, test the claim that the treatment (drug or placebo) is independent of the reaction (whether or not headaches were experienced). Drug Placebo Headaches 11 7 No headaches 73 91 H0 : Treatment and reaction are independent. Ha: Treatment and reaction are dependent. Find 2.
A) 4.605
B) 7.815
C) 1.798
5
D) 3.841
E) 5.942
18)
19) Responses to a survey question are broken down according to gender and the sample results are given below. At the 0.05 significance level, test the claim that response and gender are independent. Yes No Undecided Male 25 50 15 Female 20 30 10
19)
H0 : Gender and response are independent. Ha: Gender and response are dependent. Find 2.
A) 3.841
B) 5.991
C) 0.579
D) 2.706
E) 6.502
Use the 2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. 20) Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05 20) significance level, test the claim that the treatment (drug or placebo) is independent of the reaction (whether or not headaches were experienced). Drug Placebo Headaches 11 7 No headaches 73 91 H0 : Treatment and reaction are independent. Ha: Treatment and reaction are dependent. Test statistic: 2 = 1.798. State your conclusion about H0.
A) No conclusion can be made. B) Reject Ha. C) Do not reject Ha .
D) Reject H0.
E) Do not reject H0 .
21) 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 5 percent level of significance is to be used to test the null hypothesis that age and preferred music type are independent. H0 : Age and preferred music type are independent. Ha: Age and preferred music type are dependent. Test statistics 2 = 12.954 State your conclusion about H0.
A) Accept Ha . B) Reject H0.
C) Fail to reject H0.
D) Reject Ha.
E) No conclusion can be made.
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21)
Provide an appropriate response. 22) In a chi-square test of homogeneity of proportion we test the claim that A) the proportion of individuals with a given characteristic doesn't change over time. B) across a single sample the proportion of individual with the same characteristic is the same as the population. C) different populations have the same proportions of individuals with the same characteristics. D) different populations have equal means. E) the proportion of a population having a given characteristic is based on the homogeneity of the population. 23) 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. Test the hypothesis at the 0.05 level that the proportion of wins is the same for teams wearing suits as for teams wearing jeans. Win Loss Suit 22 28 T-shirt 28 22 H0 : The proportion of wins is the same for teams wearing suits as for teams wearing jeans.
22)
23)
Ha: The proportions are different. Test statistic: 2 = 1.440. Critical value: 2 = 3.841. State your conclusion about null hypothesis. A) No conclusion can be made. B) Reject H0.
C) Reject Ha.
D) Fail to reject Ha. E) Fail to reject H0.
24) 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 Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges. H0 : The proportion of students smoking is the same at all four colleges. Ha: The proportions are different. Test statistic: 2 = 17.832. Critical value: 2 = 11.345. State your conclusion about the null hypothesis. A) No conclusion can be made. B) Reject H0.
C) Fail to reject H1.
D) Reject H1.
E) Fail to reject H0.
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24)
Answer Key Testname: CH11PRAC 1) A 2) A 3) D 4) A 5) D 6) B 7) B 8) B 9) D 10) C 11) D 12) A 13) E 14) B 15) B 16) A 17) A 18) C 19) C 20) E 21) B 22) C 23) E 24) B
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