The following table gives the results of flower color and type of leaf. Flower Color Flat Curled Pink 2 30 Red 9 12 Examine the vaccine has a effect in controlling the disease

Solution:

Problem to test:

Null Hypothesis(H0): There has no effect in controlling the disease

Alternate Hypothesis(H1): There has effect in controlling the disease

Test Statistics:

Since, this is the case of 2 by 2 table and one shell frequency is less than 5 then we have formula,

$$X_{cal}^2 = \frac{N[(ad – bc) – \frac{N}{2}]^2}{(a+b)(c+d)(a+c)(b+d)}$$

For calculation of X2

 Flower Color Flat Curled Total Pink 2   (a) 30   (b) 32   (a+b) Red 9   (c) 12   (d) 21   (c+d) Total 11   (a + c) 42   (b + d) 53  (a+b+c+d = N)

Now,

$$X_{cal}^2 = \frac{53.[(2 \times 12 – 30 \times 9) – \frac{53}{2}]^2}{32 \times 21 \times 11 \times 42}$$

$$= \frac{3935581.25}{310464}$$

= 12.67

Critical Value: The tabulated value of X2 at 0.05 level of significance with (2-1)(2-1) = 1 d.f. is $$X_{(0.05, 1)}^2 = 3.841$$

Decision: Since $$X_{cal}^2$$ = 12.67 > $$X_{tab}^2$$ = 3.841. So, H1 is accepted and H0 is rejected.

Conclusion: Hence, There has effect in controlling the disease.