Question

An executive had run a test of hypothesis and reported that there was a significant increase in the sales when he used alpha level 8%, presumably, he performed a hypothesis test against the null hypothesis of no change in sales. Had he used alpha level 5%, his reports that the sales increased significantly would have been with a. more error b. less power c. Less Confidence d. more power.

Answer 1

An alpha level is the probability of a type I error, or you reject the null hypothesis when it is true.

We can always control the alpha level.

So if the alpha is 5% then we can say the confidence level is 95% i.e if we perform an experiment 100 times, 95 times the true value of the concerned parameter will lie within the certain range.

As the alpha level is the probability of making a Type I error, we can make this area as tiny as possible.

A tiny area means there is less chance in rejecting the true null hypothesised i.e less chance of making type I error. But this increases the chance of committing type II error ( accepting false null hypothesis).

Again power of a test =1-P(type II error)

So as type II error increases, power of the test decreases.

So at alpha =8% it was found that there was significant increase of sales against null hypothesis of no change in sales.

If it had been alpha = 5%, alpha is made less which indicates type I error would be smaller than previous which further indicates type II error increases which implies power of the test will be less than that of previous.

So his conclusion of the increase in sales would be with less power.

Hence, option (a) is not correct as more error does not specify if it is type I or type II error (one error increases, another decreases).

Option (c) less confidence is not correct as confidence level is increasing from 92 to 95%

The power also becomes less so option (b) less power is correct