Question

A recent poll of 2100 randomly selected 18-25-year-olds revealed that 243 currently use marijuana or hashish. According to a publication, 12.6 % 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 12.6%? Use α=0.05 significance level.

test statistic z=

positive critical zz score

negative critical zz score

Answer 1

Given that, n = 2100 and x = 243

=> sample proportion = 243/2100 = 0.115714

The null and alternative hypotheses are,

H0 : p = 0.126

Ha : p ≠ 0.126

This test is two-tailed.

Test statistic is,

=> Test statistic is, Z = -1.42

Using standard normal z-table we get, critical values at significance level of α=0.05 are, Z^* = ±1.96

=> Positive critical z score = 1.96

=> Negative critical z score = -1.96

​​​​Since, test statistic = -1.42 > -1.96, we fail to reject the null hypothesis (H0).