In a classic study of peptic ulcer blood hypos wore determin

In a classic study of peptic ulcer, blood hypos wore determined for 1,655 ulcer patients. The minitab output below shows the data for those and for an independently chosen group of 10,000 healthy controls from the same city. Note that several entries in the output have been hidden by *\'s. Compute the missing entry *E*, **F**, and DF in the output. Carefully state the null and alternative hypotheses H0 and HA. Give your decision about the test result at the significance level of 0.01. Give your conclusion in the context of research.

Solution

Given that in a classic study of peptic ulcer, blood types were determined for 1655 ulcer patients.

For an independently chosen group of 10000 healthy controls from the same city.

Here we have to test the hypothesis that,

H0 : The two groups ulcer and control are independent.

H1 : The two groups ulcer and control are not independent.

The test statistic for testing H0 and H1 is,

² = (O - E)² / E

where O is observed frequency.

and E is the expected frequency.

Given that observed frequencies and from observed we have to calculate some expected frequencies.

The formula for Expected frequencies is,

E = (row total) * (column total) / sample size

sample size = 11655

For 579,

E = (4798 * 1655) / 11655 = 681.31

For 124,

E = (1014 * 1655) / 11655 = 143.99

For 4219,

E = (4798*10000)/11655 = 4116.69

So the complete table for observed frequency and expected frequency is,

degrees of freedom = (R-1)*(C-1)

where R = number of rows = 2

C = number of columns = 4

degrees of freedom = (2-1)*(4-1) = 1 * 3 = 3

Calculate P-value for taking decision is,

P-value =

=chiinv(x , d.f.)

where x is the test statistic value.

d.f. = 3

P-value = 1.29457E-10 = 0.0000

given that alpha = level of significance = 0.01

P-value < alpha

reject H0 at 1% level of signifcance.

Conclusion :

The two groups ulcer and control are not independent.

blood type	O	A	B	AB	total
ulcer	911	579	124	41	1655
control	4578	4219	890	313	10000
total	5489	4798	1014	354	11655