In mid-2016 the United Kingdom (UK) withdrew from the European Union (an event known as ?Brexit?), causing economic concerns throughout the world. One indicator that economists use to monitor the health of the economy is the proportion of residential properties offered for sale at auction that are successfully sold. An article titled ?Going, Going, Gone through the Roof?Sky?s the Limit at Auction? (estateagenttoday .co.uk/features/2016/10/going-going-gone-through -the-roof--the skys-the-limit-at-auction, October 22, 2016, retrieved May 4, 2017) reported the success rate of a sample of 26 residential properties offered for sale at auctions in the UK in the summer of 2016. For this sample of properties, 14 of the 26 residential properties were successfully sold. Suppose it is reasonable to consider these 26 properties as representative of residential properties offered at auction in the post-Brexit UK.

a. Would it be appropriate to use the large-sample confidence interval for a population proportion to estimate the proportion of residential properties successfully sold at auction in the post- Brexit UK? Explain.

b. Would it be appropriate to use a bootstrap confidence interval for a population proportion to estimate the proportion of residential properties successfully sold at auction in the post-Brexit UK? Explain.

c. Use the accompanying output from the ?Bootstrap Confidence Interval for One Proportion? Shiny app to report a 95% bootstrap confidence interval for the population proportion of residential properties successfully sold at auction in the post-Brexit UK. Interpret the confidence interval in context.

d. The success rate for properties sold at auction throughout the UK during one stretch a year earlier?in 2015?was 72%. Does this value fall within the bootstrap confidence interval reported in Part (c)? What does this indicate?

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Bootstrap Distribution 200 150 100 50 0.2 0.5 Sample Proportion 0.6 0.7 0.8 Observed Sample Proportion Lower Bound Upper Bound Conf Level *of Bootstrap Samples 1000 Standard Error 0.538 0.100 0.346 0.731 96% ADuanba