Question

(1 point) A recent poll of 2300 randomly selected 18-25-year-olds revealed that 266 currently use marijuana or hashish. According to a publication, 12.5% of 18-25-year-olds were current users of marijuana or hashish in 1997. Do the data provide sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%? Use α=0.01 significance level.

test statistic z=

positive critical z score    

negative critical z score     

The final conclusion is

A. There is not sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.
B. There is sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ : p = 0.125

H_a : p 0.125

n = 2300

x =266

= x / n = 266 / 2300 = 0.1157

P₀ = 0.125

1 - P₀ = 1 - 0.125 = 0.875

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1157 - 0.125 / [(0.125 * 0.875) / 2300]

= -1.356

Test statitic = -1.356

= 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Positive critical value = +2.576

Negative critical value = -2.576

Test statitic > critical value

-1.356 > -2.576

Reject the null hypothesis .

B. There is sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.