Im having some trouble figuring out this question from my ho

I\'m having some trouble figuring out this question from my homework:

True, False, Uncertain with Explanation:

3. There are 20 stores along Madison Avenue. I want to estimate the effect of weather on sales at the stores, so I run one regression for each store. In each I regress sales on weather conditions. Claim: I would expect to get one slope coefficient significantly different from zero at the 5% level even if all the true (population) slope coefficients are zero.

Solution

3) True. This is true irrespective of regression, because this is property of p-value. Since p-value of 0.05 means probability of getting this extreme sample under null, we expect to get p-value of below 0.05 in 5% of cases, in other words, we get 1 out of 20 tests significant at 5% level even if all tests have null hypothesis true.