Final answer:
To determine if cloud unseeding leads to significantly more rainfall, we can carry out a hypothesis test using a one-sided t-test for independent samples. We need to calculate the t-statistic and compare it to the critical value at the 2% significance level.
Step-by-step explanation:
To determine if cloud unseeding leads to significantly more rainfall, we can carry out a hypothesis test. Let's define the null hypothesis H0: the mean amount of rainfall from seeded clouds is equal to the mean amount of rainfall from unseeded clouds. The alternative hypothesis Ha: the mean amount of rainfall from seeded clouds is significantly greater than the mean amount of rainfall from unseeded clouds.
We can use a one-sided t-test for independent samples to compare the means of the two groups. We have data on rainfall from 26 seeded clouds and 26 unseeded clouds. Calculate the mean and standard deviation of the rainfall in each group. Next, calculate the t-statistic using the formula: t = (mean_seeded - mean_unseeded) / sqrt((sd_seeded^2 / n_seeded) + (sd_unseeded^2 / n_unseeded)), where sd is the standard deviation and n is the sample size.
Finally, compare the calculated t-value to the critical value of a t-distribution with (n_seeded + n_unseeded - 2) degrees of freedom at the 2% significance level. If the calculated t-value is greater than the critical value, we can reject the null hypothesis and conclude that cloud unseeding leads to significantly more rainfall.