Question

Assume all data is normally distributed unless otherwise stated. Please show all steps of the work.

The use of both alcohol and tobacco by high school seniors has declined in the last 30 years. Alcohol use is down from 36.7 to 20.4%, and the use of cigarettes by high school seniors has decreased from 68.2 to 43.1%. A random sample of 300 high school seniors from a large region indicated that 82% had NOT consumed any alcohol during the 30 days prior to the survey. At the 0.05 level of significance, test the claim that the use of alcohol by high school seniors has decreased from 20.4%.

Answer 1

Since we need to find if alcohol consumption has decreased, we conduct a left tailed test = 0.05

= Proportion of students who had consumed alcohol = 1 - 0.82 = 0.18

p = 0.204

1 - p = 0.796

______________________

The Hypothesis:

H0: p = 0.204

Ha: p < 0.204

This is a Left tailed Test.

The Test Statistic:

The p Value:    The p value (Left tail) for Z = -1.03, is; p value = 0.1515

The Critical Value:   The critical value (Left tail) at = 0.05, Z critical = -1.645

The Decision Rule:

The Critical Value Method: If Z observed is <- Z critical Then Reject H0.

The p value Method: If the P value is < , Then Reject H0

The Decision:   

The Critical Value Method: Since Z observed (-1.03) is > -Z critical (-1.645), We Fail to Reject H0.

The p value Method: Since P value (0.1515) is > (0.05), We Fail to Reject H0.

The Conclusion:   There isn’t sufficient evidence at the 95% significance level to support the claim that the use of alcohol by high school seniors has reduced from 20.4%.