Waterfall Meights is there a signincant difference at $\alpha=0.10$ in the mean heights in feat of waterfals in Euroge and the ones in Asia? The dats are shown. Use the cricical value midhod wich tables.
\begin{tabular}{cc|cc}
\multicolumn{2}{c|}{ Europe } & \multicolumn{2}{c}{ Asia } \\
\hline 487 & 1246 & 614 & 320 \\
470 & 345 & 350 & 964 \\
900 & & 722 & 830
\end{tabular}
Sine dasa te Exiel
Use $14_{4}$ for the mean heght of woterfalls in turope. Assume the variables are normally distributed and the variances are unequal.
Answer
If the p-value is less than the significance level (0.10), we reject the null hypothesis and conclude that there is a significant difference in the mean heights of waterfalls in Europe and Asia. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not a significant difference in the mean heights of waterfalls in Europe and Asia.
Step 1 ：The problem is asking for a comparison of the mean heights of waterfalls in Europe and Asia. This is a two-sample t-test problem where we are comparing the means of two independent groups. The null hypothesis is that there is no difference in the means, while the alternative hypothesis is that there is a difference.
Step 2 ：We are given the data for the heights of the waterfalls in both continents and we are asked to determine if there is a significant difference at a significance level of 0.10. We are also given that the variables are normally distributed and the variances are unequal, which means we should use the Welch's t-test.
Step 3 ：The heights of the waterfalls in Europe are: 487, 1246, 470, 345, 900. The heights of the waterfalls in Asia are: 614, 320, 350, 964, 722, 830.
Step 4 ：We will calculate the t-statistic and the p-value for the Welch's t-test. The t-statistic is a measure of the difference between the two means relative to the variability of the data. The p-value is the probability of observing a t-statistic as extreme as the one calculated (or more extreme) under the null hypothesis.
Step 5 ：If the p-value is less than the significance level (0.10), we reject the null hypothesis and conclude that there is a significant difference in the mean heights of waterfalls in Europe and Asia. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not a significant difference in the mean heights of waterfalls in Europe and Asia.
