Question

A study might compare the rates of microbiologic cure of three different antibiotics used for urinary tract infection, as shown in the following table:

	Antibiotics 1	Antibiotics 2	Antibiotics 3	Total
Cure	49	112	26	187
Not cure	12	37	8	57
Total	61	149	34	244

1. Are the variables quantitative or qualitative?
2. Which statistical test is appropriate to use on these data?
3. What are the null & the alternative hypotheses, here? Use 10% level of significance
4. Carry out the hypothesis test(s) in question in above c.

Is there is a relationship between which antibiotic the patient took and achieving microbiologic cure?                

Answer 1

a)The variables are quantitive.

b)Chi sq test is appropriate in this situation.

c)H₀=all the antibiotics are equivalent vs H₁=not H₀

d)p_i=denotes that the proportion of people who are cured. for all i=1(1)2

p₁=187/244=0.77

p₂=57/244=0.23

the expected frequencies of the different classes

61*0.77=46.97	149*0.77=114.73	34*0.77=26.18
61*0.23=14.03	149*0.23=34.27	34*0.23=7.82

chi sq= double sum over j=1(1)3 and i=1(1)2 {(N_ij-n_ip_i)²/n_ip_i}

=((49-46.97)²/46.97+(12-14.03)²14.03)+

((112-114.73)²/114.73+(37-34.27)²/34.27)+

(26-26.18)²/26.18+(8-7.82)²/7.82)

=0.665

now the df is =(2-1)(3-1)=2

the tabulated chi sq with level of significnce (alpha)=0.1 and df is=2

and its value is=0.211

as we can see that the chi sq value is much greater than the tabulated value (0.665>0.211)

then we reject our null hypothesis at level 0.1.

**as we reject our null hypothesis this imply that the antibiotics has no relationship between them.