Question

1. Of 1000 randomly selected cases of lung cancer, 823 resulted in death. Is there sufficient evidence to say the true proportion of lung cancer deaths is different than 85% at a significance level of 5%. a) Are the normality assumptions satisfied? Explain why.

b) State hypotheses.

c) Calculate the test statistic

d) What is/are the critical value(s)?

e) What is your decision?

f) What is the conclusion/interpretation of this decision?

Answer 1

a)

np = 1000 * 0.85 = 850 >= 10

n(1-p) = 1000 * (1-0.85) = 150 >= 10

Since np>= 10 and n(1-p) >= 10 , the normality assumptions are satisfied.

b)

H0: p = 0.85

Ha: p 0.85

c)

Sample proportion = 823 / 1000 = 0.823

Test statistics

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

= 0.823 - 0.85 / sqrt( 0.85 * ( 1 - 0.85) / 1000)

= -2.39

d)

From Z table, critical values at 0.05 level = -1.96 , 1.96

e)

Since test statistics falls in rejection region, that is test statistics value < -1.96

so we have sufficient evidence to reject H0.

f)

We conclude at 0.05 level that we have enough evidence to support the claim that the true proportion

of lung cancer deaths is different than 85%.