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

	Shift
	Morning	Evening	Night
Influenza	11	20	11
Headache	34	37	5
Weakness	17	14	7
Shortness of Breath	8	10	10

1. Compute the expected frequencies under the null hypothesis.

2. Compute the value of the chi-square statistic. Round the answer to at least three decimal places. 3. how many degrees of freedom are there?

4. Test the hypothesis of independence. use the alpha =0.10 level of significance. what do you conclude?