Questions 14 - 22 concern the following idea: To investigate whether the mean weekly rental price for 2 bedroom apartments in the CBD differ between various Australian cities and economist collected data on twenty-five such apartments in the following cities: Adelaide, Melbourne, Perth and Sydney. Let # , #,, M, and u be the population mean weekly rental price (in Australian dollars [AUD]) in Adelaide, Melbourne, Perth and Sydney respectively and ?, a}, ? and 2 be the respective population variances. An ANOVA was performed on the data and some of the output is given below, with some entries obscured with ?? mean sd data:n Adelaide 454.2239 38.35095 25 Melbourne 495.9615 44. 07615 Perth 479. 3680 36.94976 Sydney 503. 8304 40. 01908 summary(AnovaModel . 1) Of Sum Sq Mean Sq F value Pr(>F) city 36067 ?? ?? 0.00014 *** Residuals ?? 153128 1595 Fit: aov(formula = rent ~ city, data = dat) Linear Hypotheses: Estimate Std. Error t value Pr(>Itl) Melbourne - Adelaide == 0 41. 738 11. 296 3. 695 0. 00194 ** Perth - Adelaide == 0 25. 144 11. 296 2.226 0. 12379 Sydney - Adelaide == 49. 607 11.296 4.391 F) group 3 0.2013 0.8953 96 To analyse whether or not the mean rental price differs between the four cities, what is the correct set of hypotheses? O a. Ho: H, =#2=13=HA Ob. Ho : H, =/2 = 1 3=HA H : all means are different Oc. Ho : H, =12 = 1 3=HA H : all means are not equal O d. Ho : H, =H2=13=H4 H : not all means are equalRefer to the ANOVA in Question 14 to answer this question: What is the missing number in the Df column for Residuals?Refer to the ANOVA in Question 14 to answer this question: Calculate the observed value of the ANOVA test statistic (correct to 3 decimal places). Refer to the ANOVA in Question 14 to answer this question: Read the pvalue from the ANOVA table. Which of the following is the correct decision and conclusion based on that pvalue (use o=0.05}? O a. pvalue > 0.05. so there is no signicant evidence against the null hypothesis and we conclude that there is no evidence to suggest thatthe weekly mean rental price differs between these citles. O b. pvalue 0.05. so there is signicant evidence against the null hypothesis and we conclude that the weekly mean rental price dill'ers between these cities. 0 e. pvalue 0.05 we can reject H1, meaning that there is significant evidence to support the idea of equal variance. O b. p > 0.05 we can reject Ho, meaning tlhat here is significant evidence against the idea of equal variance. 0 c. p 0.05 so we cannot reject H0, meaning that there is no signicant evidence against the idea ofequal variance. 0 d. p > 0.05 so we cannot reject H0. meaning that there is no signicant evidence against the idea of equal variance. C) e. p C 0.05 so we reject Ho, meaning that there is signicant evidence to support the idea of equal variance. Refer to the ANOVA in Question 14 to answer this question: If we examined a qqplot of the residuals, which of the following best describes what we would be looking for? O a. We would want to see the points roughly fall along the straight line, which would help support the assumption of normality. O b. We would want to see a roughly bell shaped graph, which would help support the assumption of normality. O c. We would want to see the points roughly fall in lines of the same height, which would help support the assumption of equal variance. O d. We would want to see a patternless spread of points across the graph, which would help support the assumption of equal variance.Refer to the ANOVA in Question 14 to answer this question: Part of the ANOVA output above is the Tukey multiple comparison of means. Using this Tukey output, which of the following would be the correct conclusion when summarising the analysis? O a. Mean weekly rental prices in Adelaide are significantly lower than in all other cities as it has the lowest sample mean. O b. The mean weekly rental prices between Melbourne and Sydney do not differ significantly (p=0.898), but the mean weekly rental prices in those two cities are significantly higher than the mean weekly rental price in Perth. In turn, the mean weekly rental price in Perth is significantly higher than the one in Adelaide. O c. Mean weekly rental prices in Sydney are signficantly larger than in all other cities as it has the highest sample mean. O d. There is no significant difference between the mean weekly rental prices in Melbourne, Perth and Sydney. There is also no significant difference between the mean weekly rental prices in Adelaide and Perth, however the mean weekly rental price in Adelaide differs significantly from those in Melbourne and Sydney with Adelaide having the lower mean weekly rental price.Refer to the ANOVA in Question 14 to answer this question: If I was to calculate a 95% CI for the mean weekly rental price in Adelaide, what would he the standard deviation that I used in the calculation of that condence interval? 0 a. 44.0?6 0 b. 33.351 0 c. 36.95 C) d. 39.93? C) e. 40.019 Refer to the ANOVA in Question 14 to answer this question: Assume that the unadjusted 95% confidence interval for the mean weekly rental price in Perth has been calculated as ($463.5, $495.22). An analyst is wondering if there was significant evidence that the mean weekly rental price in Perth is different from $470. Just using the confidence interval, what would be the correct conclusion be (use a = 0.05)? O a. We have only been provided with a confidence interval, so cannot make this type of conclusion. O b. Since $470 is within the confidence interval, there is significant evidence that / , is different from $470. O c. The majority of the confidence interval is greater than $470, so there is significant evidence that u , > 470. O d. Since $470 is within the confidence interval, there is no significant evidence that u , is different from $470