A survey found that the average hotel room rate in New Orleans is $88.42 and the average room rate in Phoenix 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?

As we are testing here whether the hotel stays are cheaper in Phoenix, the test statistic here is computed as:

$z^{*}=\frac{\bar{X}_{1}-\bar{X}_{2}}{\sqrt{\frac{\sigma_{1}^{2}+\sigma_{2}^{2}}{n}}}=\frac{80.61-88.42}{\sqrt{\frac{5.62^{2}+4.83^{2}}{50}}}=-7.4524$

As the test statistic value here is very low, therefore the p-value here would be approximately equal to 0 and therefore the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that the hotel stays are cheaper in phoenix.

p-value is close to 0 < 0.01 which is the level of significance.