Question

briefly describe the different steps in constructing a hypothesis test (law suitability) using a 90% confidence level chi-square test. for that we suppose to work with a sample of 200 realizations of a random variable. we can consider 5 classes

Answer 1

Steps in hypothesis construction for a chi square test -

1. Set confidence level (90% in this case)

2. Set up null and alternate hypothesis for test -

(Assume we have 2 gender (Male and Female) and 5 classes and that the hypothesis we are trying to test is for heart rate)

Null hypothesis - Heart rate proportion for classes is independent of gender

Alternate hypothesis - Heart rate proportion for classes is not independent of gender

3. Note observed and expected values of classes for gender types

The table should look like -

	Class 1	Class 2	Class 3	Class 4	Class 5	Total
Male	a	b	c	d	e	a + b + c + d + e
Female	f	g	h	i	j	f + g + h + i + j
Total	a + f	b + g	c + h	d + i	e + j	a + b + c + d + e +f + g + h + i + j = N

for cell a the expected value would be (a+b+c+d+e)(a+f)/N

4. Calculate chi square test statistic

Observed	Expected	|O - E|	(O — E)2	(O — E)2/ E

chi sq statistic = Sum (O-E)² over all observed values

5.

Look up the critical value at (row-1) * (column - 1) degrees of freedom and 0.1 significance level.

6.

If, chi sq statistic > critical vale, reject the null hypothesis and conclude that -

gender and classes are not independent