The website www.domain.com.au lists houses for sale in Australia. The asking prices of established houses with 4 bedrooms, 2 bathrooms and 2 car spaces for sale in August 2009 in Bundaberg (central and adjoining suburbs), Queensland 4670 and Gympie, Queensland 4570 are given in the table (in thousands of dollars). All listings have been accounted for and duplicate listings by different real estate agents have been removed; therefore, the data constitute the population. Listings without a proper address or asking price have been excluded. Assuming normality:

(a) test the hypothesis that the mean house prices in the two Queensland cities are not significantly different; use ? = 0.05

(b) construct a 95% confidence interval for the difference between mean house prices in Bundaberg and Gympie.

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Bundaberg house prices ($000) 349 279 299 309 Gympie house prices ($000) 749 365 389 585 495 449 439 442 475 359 300 315 312 379 340 339 334 370 329 399 339 349 334 299 295 305 348 329 289