Question

Exercise 3. Suppose we would like to test the hypothesis that at least 10% of students suffer from allergies. We collect a random sample of 225 students and 21 of them suffer from allergies. (a) State the null and alternative hypotheses. (b) Obtain a test statistic and a p-value. (c) State the conclusion at the a = 0.05 level.

Answer 1

3)

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p < 0.10

$\hat p$ = x / n = 21 / 225 = 0.0933

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.0933 - 0.10 / [$\sqrt$(0.10 * 0.90) / 225]

= -0.333

P-value = 0.3694

$\alpha$ = 0.05

P-value < $\alpha$

Fail to reject the null hypothesis .