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different weekdays with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

TEST THE APPROPRIATE HYPOTHESIS. Include the null and alternate hypotheses, degrees of freedom, test statistic, rejection region, and decision.

Perform the indicated goodness-of-fit test.

1) In studying the occurrence of genetic characteristics, the following sample data were

 1)obtained. At the 0.05 significance level, test the claim that the characteristics occur with the same frequency.

Characteristic A        B     C     D     E      F
Frequency 28 30 45 48 38 39

2)   A company manager wishes to test a union leader's claim that absences occur on the 

2) different weekdays with the same frequencies. Test this claim at the 0.05 level of significance if the following

sample data have been compiled.

Day Mon Tue Wed Thur Fri
Absences 37     15       12      23     43

3). Using the data below and a 0.05 significance level, test the claim that the responses occur

3) with percentages of 15%, 20%, 25%, 25%, and 15% respectively

Response A B   C D E
Frequency 12 15 16 18 19

4). You roll a die 48 times with the following results

Number 1 2 3 4 5 6
Frequency 4 13 2 14 13 2

Use a significance level of 0.05 to test the claim that the die is fair.

Use a Λ2 test to test the claim that in the given contingency table, the row variable and the column variable are independent.

1)   Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05 5) significance level, test the claim that the treatment (drug or placebo) is independent of the action (whether or not headaches were experienced).

Drug Placebo
Headaches 11               7
No headaches 73             91

 

6) 160 students who were majoring in either math or English were asked a test question, and the 6) researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent.
Correct Incorrect
Math 27               53
English 43               37

7)   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 types are independent. 

Solve the problem.

8)   At a high school debate the tournament, half of the teams were asked to wear suits and ties   

8)  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

9)   A researcher wishes to test the effectiveness of flu vaccination. 150 people are vaccinated, 9) 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

Use a 0.05 significance level to test the claim that the proportion of people catching the flu is the same in all three groups

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