Question

1. A survey of contraceptive methods conducted by the National Center for Health Statistics in 1965 indicated that among 30-39 year old, married, nonpreganant women who practiced contraception 20% used some form of permanent contraception. The frequency of use of permanent contraception is suspected to have changed over the next 4 decades. To test this hypothesis, records were selected of 50 women subscribing to prepaid health plans in 2005 who were 30-39 year old, married, nonpreganant and practiced contraception. From these records 16 used some form of permanent contraception. Suppose we wish to test the hypothesis that a change has occurred in the true proportion of women who use permanent contraception withoutspecifying the direction of that change. Suppose researchers are willing to commit the error of mistakenly rejecting the null hypothesis only 1% of the time.

1. What is the significance level in this problem?
2. Specify the null and alternative hypothesis
3. Carry out the steps of the hypothesis test (calculate test statistic, p-value, and make a decision).
4. If the true proportion of permanent contraception in 2005 was really0.32, what is the power of this test with a sample size of 50. Use the SAS code below but be sure to fill in the place that are blank

procpower;

onesamplefreqtest=z method=normal

alpha=

nullproportion=

proportion=

sides= 2

ntotal= 50

power= .;

run;

5. What sample size would you need in order to ensure that your Type II error is 20%. Use the above SAS code –you will need to modify the code so it calculates n instead of the power.

Answer 1

It will be solved using two-tailed test on proportions, as given below:

Using z-table, area under z= -3.815 is approx. 0

and area under z=0.176 =0.5699 =

Therefore, power of test = 1- = 1-0.5699 = 0.43