Question

A researcher was conducted to test the effect of a new drug on viral infection. The infection was put on a group of mice and the mice was randomly split into two groups, different groups. The first group (control group), received no treatment for the infection. The second group received the drug. After a 30-day period, the number of survivors in the two groups were observed, and the test statistic was calculated to be z  =  1.46. If we wish to test the following hypothesis, H0 : p1  =  p2     vs     H1 : p1  ≠  p2, what is the p-value?

Answer 1

Solution:

Given:

The first group (control group), received no treatment for the infection.

The second group received the drug.

After a 30-day period, the number of survivors in the two groups were observed, and

the test statistic was calculated to be z = 1.46.

Hypothesis are:

H₀ : p₁  =  p₂     vs     H₁ : p₁  ≠  p₂,

We have to find the p-value:

Since alternative hypothesis H1 is not equal to type ( ≠ ), this is two tailed test.

Thus p-value is:

p-value = 2 X P( Z > z ) if z test statistic is positive.

and p-value = 2 X P( Z < z ) if z test statistic is negative.

p-value = 2 X P( Z > 1.46 )

p-value = 2 X [ 1 - P( Z < 1.46 ) ]

Look in z table for z = 1.4 and 0.06 and find corresponding area.

Thus P( Z > 1.46 ) = 0.9279

Thus

p-value = 2 X [ 1 - P( Z < 1.46 ) ]

p-value = 2 X [ 1 - 0.9279 ]

p-value = 2 X 0.0721

p-value = 0.1442