Question

. Consider the following hypothesis test: H0 : µ ≥ 20 H1 : µ < 20 A sample of 40 observations has a sample mean of 19.4. The population standard deviation is known to equal 2. (a) Test this hypothesis using the critical value approach, with significance level α = 0.01. (b) Suppose we repeat the test with a new significance level α ∗ > 0.01. For each of the following quantities, comment on whether it will change, and if so, in what direction? i. the critical value ii. the probability of a Type I Error iii. the probability of a Type II Error iv. the p-value

Answer 1

Ans:

a)

z=(19.4-20)/(2/sqrt(40))

z=-1.897

critical z value=-2.326

Fail to reject the null hypothesis.

b)

i)critical value will change,it will increase (i.e. from more negative to less negative direction)

ii)Probability of type I error=alpha

So,if alpha increase,type I error increase.

iii)If alpha increase,we will be more likely to reject the null hypothesis,so probability of type II error decrease.

iv)p-value will not change,as it depends on the sample statistic.