Question

State the null and alternative hypotheses. Design a proper testing procedure. Calculate test statistic, rejection region and p-value.

Among patients with lung cancer, usually, 90% or more die within three years. As a result of new forms of treatment, it is felt that this rate has been reduced. In a recent study of n = 150 lung cancer patients, y =128 died within three years. Is there sufficient evidence at the α = 0.05 level, to conclude that the death rate due to lung cancer has been reduced?

Answer 1

H0: p >= 0.90

Ha: p < 0.90

Sample proportion = 128 / 150 = 0.8533

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.8533 - 0.90) / sqrt ( 0.90 * ( 1 - 0.90) / 150)

= -1.91

This is test statistics value.

From Z table,

Critical value at 0.05 significance level = -1.645

Rejection region = Reject H0, if z < -1.645

Since test statistics falls in rejection region, reject H0.

p-value = P(Z < z)

= P(Z < -1.91)

= 0.0281 (From Z table)