Question

One research study of illegal drug use among​ 12- to​ 17-year-olds reported a decrease in use​ (from 11.4% in​ 1997) to 9.8 ​% now. Suppose a survey in a large high school reveals​ that, in a random sample of 1 comma 058 ​students, 96 report using illegal drugs. Use a 0.05 significance level to test the​ principal's claim that illegal drug use in her school is below the current national average. Formulate the null and alternative hypotheses. Choose the correct answer below.

Answer 1

H0: P = 0.098

H1: P < 0.098

= 96/1058 = 0.0907

The test statistic is

= -0.80

P-value = P(Z < -0.80)

= 0.2119

Since the p-value is greater than the significance level(0.2119 > 0.05), so we should not reject the null hypothesis.

At 0.05 significance level, there is not sufficient evidence to support the principal's claim that illegal drug use in her school is below the current national average.