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StatisticsQ&A LibraryA 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?Question

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?

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:

H_{0}: the work shift and various symptoms are independent.

H_{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:**

Step 2

**The formula for expected frequency is,**

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

Step 3

**b.**

**The value of test statistics is obtained below:**

The formula for chi-square test statistics is

= (Observ...

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