Question

The proportion of smokers among adult residents of California in 2017 was 11.8%, one of the lowest in the United States. A statistics student thought that the proportion of smokers will be lower. He took a random sample of 400 adults and found that 31 of them smoke. Did he have enough evidence to conclude that the percentage of adult smokers in California is lower than 11.8%.

Answer 1

Solution :

This hypothesis test is a left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.118

H_a : p < 0.118

= 31 / 400 =  0.0775

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0775 - 0.118 / [(0.118 * 0.882) / 400]

= -2.51

P-value = 0.006

= 0.05

P-value <

Reject the null hypothesis .

There is enough evidence to suggest that the percentage of adult smokers in California is lower than 11.8%.