Question

A certain drug can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux. The manufacturer of the drug claims that more than 93​% of patients taking the drug are healed within 8 weeks. In clinical​ trials, 208 of 221 patients suffering from acid reflux disease were healed after 8 weeks. Test the​ manufacturer's claim at the alpha equals 0.1 level of significance. Find the test​ statistic, z 0.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.93

H_a : p > 0.93

= x / n = 208/221 = 0.9412

P₀ = 0.93

1 - P₀ = 1-0.93 = 0.07

Test statistic = z 0

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.9412 -0.93 / [0.93*(0.07) /221 ]

= 0.65

P(z > 0.65 ) = 1 - P(z < 0.65 ) = 0.2575

P-value = 0.2575

= 0.1    

p=0.2575 ≥ 0.1

The null hypothesis is not rejected.

There is not enough evidence to claim that the population proportion p is greater than p₀​, at the α=0.1 significance level