Question

one sample showed that among 780 randomly selected students who completed four years of college 20% smoke. Use a=0.02 significance level to test the claim that the rate of smoking among those four years of college is less than 27% rate for the general population

Answer 1

Null hypothesis

H0: p = 0.27

Alternative hypothesis

H1: p < 0.27

We have for given example,

Population proportion value is =0.27

x=156

n=780

Level of significance = 0.02

One-tailed Test (lower)

Lower Critical Value -2.05

Estimate for sample proportion = 0.2

Z test statistic formula for proportion

p-value 0 approximately

Decision:Reject H0

Conclusion: We have sufficient evidence to say that, the rate of smoking among those four years of college is less than 27% rate for the general population