A survey of contraceptive methods conducted by the National Center for Health Statistics in 1965 indicated that among 30-39 year old, married, nonpregnant 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, nonpregnant 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 without specifying the direction of that change. Suppose researchers are willing to commit the error of mistakenly rejecting the null hypothesis only 1% of the time.What is the significance level in this problem?Specify the null and alternative hypothesisCarry out the steps of the hypothesis test (calculate test statistic, p-value, and make a decision).If the true proportion of permanent contraception in 2005 was really 0.32, what is the power of this test with a sample size of 50.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A survey of contraceptive methods conducted by the National Center for Health Statistics in 1965 indicated that among 30-39 year old, married, nonpregnant 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, nonpregnant 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 without specifying the direction of that change. Suppose researchers are willing to commit the error of mistakenly rejecting the null hypothesis only 1% of the time.
What is the significance level in this problem?
Specify the null and alternative hypothesis
Carry out the steps of the hypothesis test (calculate test statistic, p-value, and make a decision).
If the true proportion of permanent contraception in 2005 was really 0.32, what is the power of this test with a sample size of 50.

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