Answer to Question #5942 in Statistics and Probability for moe dawn

Question

null hypothesis that dancing does not cause rain. If the probability of it raining on a given day is 25% (irrespective of any dancing), how many successive days of rain would be needed to be able to reject the null hypothesis at a 0.01 level of significance, and thus convince that it is wrong?
how many successive days of rain would be need at a 0.05 sig level to be able to reject the null hypothesis?

Answer 1

Let N be a number of successive days of rain. We can find N using chi-squared
test. Number of degrees of freedom equals 1 and corresponding values in a table
for chi-square distribution (for 0.01 and 0.05 levels) are 6.64 and 3.84 .
Chi-squared statistics equals 3N and 3N>6.64 or 3N>3.84 to reject null
hypothesis. So we need 3 or more successive days of rain to reject the null
hypothesis at level 0.01 and 2 or more successive days to reject it at level
0.05.