Question

1. A doctor claims that 30% of patients only have a cold. During one month, the doctor finds that 112 of 420 patients only has a cold. At α=0.06, can the doctor support the claim? Write the hypotheses, the p-value, conclusion, and implication for the claim.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.30

H_a : p 0.30

n = 420

x = 112

= x / n = 112 / 420 = 0.2667

P₀ = 0.30

1 - P₀ = 1 - 0.30 = 0.70

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2667 - 0.30 / [(0.30 * 0.70) / 420]

= -1.49

Test statistic = -1.49

P(z < -1.49) = 0.0681

P-value = 2 * 0.0681 = 0.1362

= 0.06

P-value >

Do not reject the null hypothesis .