題組內容

二、統計部分：(50分)
(如有需要，可參考下列數值： \( Z_{0.05} = 1.65 \)，\( Z_{0.025} = 1.96 \)，\( \chi^{2}_{0.1, 2} = 4.605 \)，\( \chi^{2}_{0.05, 2} = 5.99 \)，\( \chi^{2}_{0.1, 3} = 6.25 \))

3. A survey found that the average hotel room rate in Taipei is $88.42 and the average room rate in Chiayi is $80.61. Assume that the data were obtained from two samples of 50 hotels each and that the standard deviations of the populations are $5.62 and $4.83, respectively. At α = 0.05, can it be concluded that there is a significant difference in the rates?(10分)