Answer to Question #224530 in Statistics and Probability for sandra

Question

Are all employees equally proven to having accidents? To investigate this hypothesis, Parry (1985) looked at a light manufacturing plant and classified the accidents by type and by age of the employee.

AgeAccident (sprain)Accident (burn)Accident (cut)    Under 25917525 and over611312

 

Answer 1

Whole problem

It is needed to test, whether the all employees equally prone to having accidents.

The null and alternative hypotheses for the test are:

H₀: Accident type seem to be independent of age.

H₁: Accident type does not seem to be independent of age.

The expected frequency formula for a particular cell:

Expected frequency $= \frac{Row \; total \times Column \; total}{Overall \; frequency}$

Consider O_i is the observed frequency for i^th cell and E_i is the expected frequency for i^th cell. There are total 2 rows (r) and 3 columns (c).

The chi-square test:

$χ^2 = \sum \frac{(O_i -E_i)^2}{E_i}$

Degree of freedom (r-1)(c-1)

$χ^2 = 20.78 \\ df = (2-1)(3-1)=2$

Consider that the level of significance is α = 0.05.

Using the Excel formula =CHISQ.DIST.RT(20.78,2) the P-value is approximately 0.

Decision rule:

If P-value is less than or equal to the level of significance, then reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Since the P-value of 0 is less than the level of significance of 0.05, reject H₀.

Thus, there is enough evidence to conclude that accident type does not seem to be independent of age, at 5% level of significance.

Correct option is C.