In: Math
Please show your calculations and steps. 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.