# Standard Deviation

Question

According to a high-profile realtor, houses in the sleepy town of Sun Beach have shown   higher appreciation over the past three years than have houses in the   bustling town of North Arden. To test the realtor’s claim, an economist has   found fifteen recently sold homes in Sun Beach and fifteen recently sold   homes in North Arden that were owned for exactly three years. The following   table gives the appreciation (expressed as a percentage increase) for each of   the thirty houses.

Appreciation rates in percent

Sun Beach 11.1, 8.5, 13.6,   8.3, 5.6, 12.3, 13.6, 6.9, 16.3, 9.1, 13.3, 14.5, 13.2, 11.4, 11.5

North Arden 9.6, 10.4, 10.8,   10.7, 10.0, 9.9, 7.6, 8.9, 11.6, 8.6, 9.0, 5.1, 10.0, 8.6, 10.2

Send data to Excel.

Assume that the two populations of appreciation rates are normally distributed and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that houses in Sun Beach have higher appreciation over the past three years than houses in North Arden?   Perform a one tailed test

A. null hypothesis

B. alternative hypothesis

C. type of test statistic if then degrees of freedom?

D. Value of test statistic

E. Critical value at 0.05 level of significance

F. Can we conclude that houses in Sun Beach have higher appreciation over the past three years than houses in North Arden?

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