It is rumoured thatthe Bank of Canada will increase interest rates next year [1]. Suppose a survey is conducted by a polling organization, and Saskatchewanians answered the question: "are you not at all concerned, somewhat concerned, or very concerned that interest rates will climb?". The results are given below.

Not at all concerned	Somewhat concerned	Very concerned
3300	1450	5250

The same survey was conducted in Ontario, and it was found that 38% of Ontarians were not at all concerned, 12% were somewhat concerned, and 50% were very concerned. The polling organization is interested in determining if the proportions of people who are not at all concerned, somewhat concerned, or very concerned about interest rates rising are the same in Saskatchewan as they are in Ontario. Conduct an appropriate hypothesis test by filling in the blanks below. Let group 1 be the "not at all concerned" group; group 2 be the "somewhat concerned" group, and group 3 be the "very concerned" group.

1) [1 mark] State the null and alternative hypotheses using the appropriate notation.

6) [19 marks] Conduct a follow-up analysis. Show all of your work.Do exactly as shown in the Module 8 Tutorial (copy/paste from that document and change numbers and context). Ensure you have the entire follow-up analysis (i.e., everything on that page, not just the table).

Example: The proportions of yearly sales across a province in Canada for five popular fruits (apples, oranges, bananas, peaches, and grapefruit, in terms of units sold to each person per year) were found to be 36 percent, 26 percent, 21 percent, 9 percent, and 8 percent, respectively. Suppose that a new survey of 1,000 shoppers in a city in that province was conducted and the following purchase frequencies were found. Test whether the city market shares differ from those of the province. Round sample proportions to 2 decimal places, and round standard errors to 4 decimal places. Conduct a follow-up analysis if applicable (round confidence interval bounds to 2 decimal places). Apples Oranges Bananas Peaches Grapefruit 391 202 275 53 79 Answer: Step 1: Ho: P1 = 0.36, p2 = 0.26, p3 = 0.21, p4 = 0.09, Ps = 0.08 Ha: at least one p; is different from its hypothesized value, for i=1,2,3,4,5. Step 2: E; = npi E1 = 1000(0.36) = 360 E2 = 1000(0.26) = 260 E3 = 1000(0.21) = 210 E4 = 1000(0.09) = 90 Es = 1000(0.08) = 80 x2 : (f. - E;)2 Ei 1=1 (f1 - E1)2 (f2 - Ez)- (f3 - E3)2 (f4 - E4)= (f5 - Es)2 + + E1 Ez E3 E4 Es (391 -360)2 (202 - 260)2 (275 - 210) (53 -90)2 (79 - 80) + + + 360 260 210 90 80 50.95056The question doesn't specify whether we have to use critical value method or pvalue method, so I'll show both to illustrate 7 in reality. you would pick your favourite method. Critical value [from Table A18): Iii1.0.05 = lines = 943773 How to get this value: look at row df=kl = 51 = 4, column 0.05 in Table A13 [posted under Week 11}. P-value {calculated using Excel): =CH|SQ.Dl5T.RT(50.95I]56, 4} = 2.28595E10 Step 4: Since the test statistic {50.95056} is greater than the critical value, we reject the null hypothesis. The rejection region was (9.4973, 00). Since the p-value [2.28595E-1D] is less than the signicance level (alpha=0.05}. we reject the null hypothesis. Step 5: At least one of the population proportions is different from its hypothesized value. This means at least one of the city market shares is different from the corresponding provincial market share. Is a followrnp analysis necessary? YES! We rejected the null hypothesis, so at least one of the population proportions is signicantly different from its hypothesized valnei but which one-(s)? That's What a followup analysis answers. Please note: I have put this 1.11 a table so you can see everything on the same page= but this is not neceswy. Step Apples Oranges Bananas Peaches Grapefruit 1 A 53 A _ 79 _ . 391 . 202 . 275 p, m 0.053 as 0.05 125 0.079 M 0.00 1.01 = 7 = 0.391 F3 0.39 332 = 7 = 0.202 N 0.20 pa = 7 = 0.275 N 0.28 1000 1000 1000 2 A 0.39(1 0.39) A 0.2(1 0.2) A 023(1 0.20) A 005(1 0.05) A 000(1 0.08) 10in 0.39, psz 0.2, pawN 0.28, 19qu 0.05, pSNN 0.00, 1000 1000 1000 1000 1000 V V V V 3519' N(0.39, 0.0154] 35294 N(0.2, 0.0126] 33394 N(0.28, 0.0142] 4~N(0.05, 0.0069] 355'\" N(0.0B, 0.0096) 3 \"(1 '1 \"(1') \"(1 '1 \"(1 '1 :51 i Zn 371 p1 F33 i Z\" 1'73 P3 354 i Z\" 374 pg :55 i Z" P5 PE 2.\" 1'1 2.\" H. i.\" 71. i.\" 11. 0.39 i 1.96(0.0154) 0.20 i 1.96(0.0126) 0.28 : 1.96(0.0142) 0.05 i 196(00069) 0.00 i 1.96(0.0006) N [0.35, 0.42] as [0.17, 0.23] m [0.25.031] N [0.03.0.07] N [0.06, 0.10] 4 We can be 95% confident that We can be 95% confident We can be 95% confident that the We can be 95% confident that We can be 95% confident that the population proportion for that the population population proportion for the population proportion for the population proportion for apples {pi} lies between 0.35 proportion for oranges (p2) bananas [pal lies between 0.25 peaches (pa) lies between 0.03 grapefruit lies between 0.06 and and 0.42. lies between 0.17 and 0.23. and 0.31. and 0.07. 0.10. 5 In the null hypothesis, we In the null hypothesis, we In the null hypothesis, we In the null hypothesis, we In the null hypothesis, we hypothesized that p1 was 0.36. hypothesized that p: was hypothesized that p3 was 0.21. hypothesized that p4 was 0.09. hypothesized that p5 was 0.08. Since 0.36 lies in the condence 0.26. Since 0.26 does not lie Since 0.21 does no! lie in the Since 0.09 does not lie in the Since 0.03 lies in the condence interval. 0.36 is a plausible value in the confidence interval, confidence interval, 0.21 is not a confidence interval, 0.09 is not a interval. 0.08 is a plausible value of pi, so we would not reject the 0.26 is not a plausible value plausible value of pa, so we would plausible value of pi, so we of pa, so we would not reject the null hypothesis that p1 = 0.36. of pz, 50 we would reject the reject the null hypothesis that p3 would reject the null hypothesis null hypothesis that p5 = 0.08. null hypothesis that p2 = 0.26. = 0.21. that p4 = 0.09. All together, we can say that the cit).r market shares are not dient from the provincial market shares for apples and grapefruit. However, since the condence intervals for oranges and peaches are entirelyr below their respective provincial market shares, the market shares for oranges and peaches inthe city are less than the market share for oranges and peaches in the province as a whole. Additionally, since the condence interval for bananas is entirely above the provincial market share, the cit).r market share for bananas is greater thanthe provincial market share