A recent study examined the effects of carbon monoxide exposure on a group of construction workers. The following table presents the number odf workers who reported various symptoms, along with the shift (morning, evening or night) that they worked.                                                         Shift                               Morning            Evening             NightInfluenza                    16                        13                    18Headache                   24                        33                      6Weakness                   11                        16                      5Shortness of Breath     7                           9                       9a. Compute the expected frequencies under the null hypothesis.b. Compute the value of chi-square statistic.c. Test the hypothesis of independence. Use the a=0.05 level of significance. What do you conclude?

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Asked Dec 1, 2019
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A recent study examined the effects of carbon monoxide exposure on a group of construction workers. The following table presents the number odf workers who reported various symptoms, along with the shift (morning, evening or night) that they worked.

                                                         Shift

                               Morning            Evening             Night

Influenza                    16                        13                    18

Headache                   24                        33                      6

Weakness                   11                        16                      5

Shortness of Breath     7                           9                       9

a. Compute the expected frequencies under the null hypothesis.

b. Compute the value of chi-square statistic.

c. Test the hypothesis of independence. Use the a=0.05 level of significance. What do you conclude?

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Expert Answer

Step 1

a.

Null and alternative hypotheses:

The null and alternative hypotheses to test whether the experimental method is superior to conventional method are independent are as follows:

H0: the work shift and various symptoms are independent.

a: the work shift and various symptoms are not independent.

Appropriate test:

The appropriate test for the given scenario is chi-square test for independence.

Decision rule:

If p-value ≤ significance level, reject the null hypothesis.

If p-value > significance level,  do not reject the null hypothesis.

The expected frequency is obtained below:

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Observed (0) Influenza Morning Evening Night Total 16 13 18 47 Headache 24 33 6 63 5 Weakness 11 16 32 Shortness of Breath 7 9 9 25 Total 58 71 38 167

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Step 2

The formula for expected frequency is,

E = (Row total) (Column total) / Grand total.

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Observed (O) Morning Night Evening 47x 58 47x 71 47x38 = 16.32 = 19.98 =10.69 Influenza 167 167 167 63x58 63x 71 63x38 =26.78 =21.88 = 14.34 Headache 167 167 167 32x58 32x38 32x71 Weakness =11.11 - 13.60 = 7.28 167 167 167 25x58 25x71 25x38 =10.63 -5.69 =8.68 Shortness of Breath 167 167 167

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Step 3

b.

The value of test statistics is obtained below:

The formula for chi-square test statistics is

= (Observ...

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(Observed count - Expected count)2/ Expected Observed Expected Chi-square (O) 16 count count 16.32 0.006 19.98 13 2.440 18 10.69 4.990 24 21.88 0.205 26.78 33 1.442 6 14.34 4.847 11 11.11 0.001 0.422 16 13.60 7.28 0.715 7 8.68 0.326 0.250 1.928 10.63 5.69 Total Chi-square 17.572

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