Question

(5 points) A recent poll of 2100 randomly selected 18-25-year-olds revealed that 243 currently use marijuana or hashish. According to a publication, 12.7 % 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 12.7%? Use a = 0.05 significance level. (Give final answers correct to *four* decimal places) 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 12.7%. 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 12.7%.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.127

H_a : p $\neq$ 0.127

$\hat p$ = x / n = 243 / 2100 = 0.1157

P₀ = 0.127

1 - P₀ = 1 - 0.127 = 0.873

Test statistic = z =

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.1157 - 0.127/ [$\sqrt$(0.127 * 0.873) / 2100]

Test statistic = z = -1.5552

$\alpha$ = 0.05

$\alpha$/2 = 0.025

Z_$\alpha$/2 = Z_0.025 ±  1.96

positive critical z-score = 1.96

negative critical z-score = -1.96

Fail to reject null hypothesis, because test statistic between -1.96 and 1.96

correct option is = A