Question

In a recent national survey, 30 Canadian adults aged 18-24 reported having used cannabis for the first time since its legalisation in 2018 compared to 68 among the 25-44-year-olds. Out of the 1500 survey respondents, 125 were 18-24-year-olds and 400 were in the 25-44 age group. The Public Health Agency has been concerned that the first time use of cannabis among the younger cohort is higher than that among the older cohort.

a) Formulate the appropriate statistical hypotheses to test if the proportion of first-time cannabis users is higher among younger adults.  

b) Perform the appropriate hypothesis test manually using the P-value approach and a 2% significance level. Make sure you verify that the relevant assumptions and conditions are met for the test.  

c) Using the corresponding confidence level, calculate a one-sided confidence interval for the difference in the proportions of first-time cannabis users among the two age groups.  

d) Are the results from b) and c) above consistent and why?

e) Use Minitab or other appropriate software to perform the calculations in b) and c) and comment on any differences.

Answer 1

a)

Let p1 is true proportion of of first-time cannabis users among younger adults and p2 is true proportion of of first-time cannabis users among older adults.

Hypotheses are:

b)

(c)

For one sided confidence interval we need one sided critical value of z. The critical value of z for 98% confidence level is -2.054.

The standard error of estimate so

For 98% confidence bound is

Since 0 is not less than -0.0175 so we fail to reject the null hypothesis.

d)

Yes results are consistent because both are testing right tailed hypothesis and confidence level is same.