Question

A recent poll of 24002400 randomly selected 18-25-year-olds revealed that 278278 currently use marijuana or hashish. According to a publication, 12.812.8 % 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 12.812.8%? Use ?=0.01?=0.01 significance level.

test statistic z=z=

positive critical zz score:

negative critical zz score:   

Answer 1

The sample proportion here is computed as:
p = x/n = 278/2400 = 0.1158

Therefore the test statistic now is computed as:

Therefore -1.7841 is the test statistic value.

As this is a two tailed test for 0.01 level of significance, we get from the standard normal tables that:

P( -2.576 < Z < 2.576 ) = 0.99

Therefore

Positive Critical value is +2.576
Negative Critical value is -2.576

Now as the test statistic value is within the non rejection region, the test is not signficant and we dont have sufficient evidence here to conclude that the the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.8%.