Question

Andrea conduct a study using 64 people in her sample however her boss thinks her sample is too small so she recruiter more people to her study until she has a sample size of 100 as her sample size increase what happens to the probability that andrea will reject a null hypothesis that is false

Answer 1

let

if we have sample mean =m

sample SD=S

sample size =n

then test statistics will be given by

so here we see that Test statistics value is directly proportional to square root of sample size "n"

Hence as we increase the value of "n" then test statistics value will become more extreme then P-Value will decrease

Hence on increasing sample P value will decrease hence chance of P-Value become less than level of significance will go up hence chance of rejecting null hypothesis will go up hence

on increasing the sample size "n" Probability of rejecting null hypothesis will increase.