Question 19 (5 points) There is increased awareness of diet choice among your friends when it comes to eating meat and dairy. You suspect that restaurants have more diet options now, but were curious if it was different between the type of restaurant (fast food vs. family restaurant). You decide to test this by randomly selecting 22 restaurants in Toronto that were not part of a franchise. You categorized them by their most stringent available diet option, and by whether they were fast food or not. The table below shows the data. Perform a Chi-square analysis of this data using the steps provided. OBSERVED No options Vegetarian Vegan Fast food 12 F . amlly 11 9 3 restaurant i. Calculate the expected counts under the null hypothesis that diet option and restaurant type are independent. Enter the values directly in the table below (report to one decimal place). ii.CompIete the table of differences (observed minus expected counts); this will help you in the next part. iii. Calculate the observed Chi-square value. Report your answer to three decimal places. iv. Find the critical Chi-square value assuming a type I error rate of 5%. Include the degrees of freedom and report your answer to two decimal places. v. Perform the statistical test. Report your statistical conclusion and explain your rationale. The following formulae and critical value table may be useful for this question. n 7 2 (Ei - Oi)2 Ei Probability Density qchisq (0.95, 1) 3. 84 qchisq (0.975, 1) 5. 02 qchisq(0.95, 2) 5.99 qchisq (0.975, 2) 7. 38 qchisq(0.95, 3) 7. 81 qchisq (0.975, 3) 9.35 qchisq (0. 95, 4) 9.49 qchisq (0.975, 4) 11. 14 qchisq(0.95, 5) 11 . 07 qchisq(0.975, 5) 12.83