Question

Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:

	Duration of Exposure
	< 1	1 to < 5	>= 5
Diseased	12	10	18
Sensitized	14	18	13
Normal	66	142	210

Part 1:

Compute the expected frequencies of diseased workers.

Part 2:

Compute the expected frequencies of sensitized workers.

Part 3:

Compute the expected frequencies of normal workers.

Part 4:

Compute for x^2

Part 5:

How many degrees of freedom are there?

Part 6:

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

State the null and alternate hypothesis.

H0:

h1:

The hypothesis test is a:

Part 7:

Find the critical value

Part 8:

Determine whether to reject H0.

Part 9:

State a conclusion.

	Duration of Exposure
	< 1	1 to < 5	>= 5
Diseased	12	10	18
Sensitized	14	18	13
Normal	66	142	210

Answer 1

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below:

	Column 1	Column 2	Column 3	Total
Row 1	12	10	18	40
Row 2	14	18	13	45
Row 3	66	142	210	418
Total	92	170	241	503