Question

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national rate of 62%. In a random survey of 340 seniors, 215 reported using (or trying) drugs or alcohol within the past 6 months. Test the claim at the 10% significance level.

Answer 1

Given that, n = 340 and x = 215

=> sample proportion = 215/340 = 0.6324

The null and alternative hypotheses are,

H0 : p = 0.62

Ha : p > 0.62

This hypothesis test is a right--tailed test.

Test statistic is,

=> Test statistic = Z = 0.47

p-value = P(Z > 0.47) = 1 - P(Z < 0.47) = 1 - 0.6808 = 0.3192

=> p-value = 0.3192

Since, p-value is greater than 0.10 significance level, we fail to reject the null hypothesis (H0).

Conclusion : There is not sufficient evidence to support the claim that the use of drugs and alcohol among local high school seniors has increased (or higher than 62%).