Question #5942

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?

Expert's answer

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.

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.

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