Consider the following hypothesis. H0: average age at first birth for mothers in

Question

Consider the following hypothesis. H0: average age at first birth for mothers in the United States is 23.7 years, and H1: average age for first-time mothers in the United States is 21 years, to be tested at the 99 percent level of confidence.

a) Is alpha known in principle? If yes, can its value be stated from the information given? if yes, what is the alpha? Please explain.

b) Is beta known in principle? If yes, can its value be stated from the information given? if yes, what is beta? Please explain

Explanation / Answer

We break the problem into information given and the hypothesis:

H0: average age at first birth for mothers in the United States is 23.7 years, and

H1: average age for first-time mothers in the United States is 21 years,

to be tested at the 99 percent level of confidence.

a) The significance level, also denoted as alpha or , is the probability of rejecting the null hypothesis when it is true. Here' the significant level of confidence is 99% , alpha and level of confidence are related.

1-alpha = level of confidence

1- alpha = .99

alpha = .01

or alpha = 1%

b)

Beta is the probability of Type II error in any hypothesis test–incorrectly concluding no statistical significance. (1 – Beta is power). This problem doesn't mention beta or the power, and hence, its value cannot be stated from the information given

I

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