The US National Survey on Drug Use and Health reports that 4.8% of persons 12 and older regu- larly use prescription pain relievers for non-medical purposes. Suppose a random sample of 900 persons who are 12 and older taken this year found 54 using them for non-medical purposes. At the a = 0.01 level of significance, has there been an increase in the true proportion of persons 12 and older that regularly use prescription pain relievers for non-medical purposes? (a) State the hypotheses for this test and define the parameter of interest in full context. (b) Verify that the assumptions for the test are met. 1. Independence Assumption, checked by the Randomization Condition: 2. Sample Size Assumption, checked by the Success/Failure Condition: (c) What are the centre and spread of the normal distribution of p under the null hypothesis? E(P) = SD(P) =

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The US National Survey on Drug Use and Health reports that 4.8% of persons 12 and older regu-
larly use prescription pain relievers for non-medical purposes. Suppose a random sample of 900
persons who are 12 and older taken this year found 54 using them for non-medical purposes. At
the a = 0.01 level of significance, has there been an increase in the true proportion of persons 12
and older that regularly use prescription pain relievers for non-medical purposes?
(a) State the hypotheses for this test and define the parameter of interest in full context.
(b) Verify that the assumptions for the test are met.
1. Independence Assumption, checked by the Randomization Condition:
2. Sample Size Assumption, checked by the Success/Failure Condition:
(c) What are the centre and spread of the normal distribution of p under the null hypothesis?
E(p)
SD(P) =
(d) Compute the test statistic for this test.
(e) Draw a rough normal diagram for this test statistic and compute the p-value for the test.
Assess the significance of this test:
(g) Make a conclusion for this test in full context.
Transcribed Image Text:The US National Survey on Drug Use and Health reports that 4.8% of persons 12 and older regu- larly use prescription pain relievers for non-medical purposes. Suppose a random sample of 900 persons who are 12 and older taken this year found 54 using them for non-medical purposes. At the a = 0.01 level of significance, has there been an increase in the true proportion of persons 12 and older that regularly use prescription pain relievers for non-medical purposes? (a) State the hypotheses for this test and define the parameter of interest in full context. (b) Verify that the assumptions for the test are met. 1. Independence Assumption, checked by the Randomization Condition: 2. Sample Size Assumption, checked by the Success/Failure Condition: (c) What are the centre and spread of the normal distribution of p under the null hypothesis? E(p) SD(P) = (d) Compute the test statistic for this test. (e) Draw a rough normal diagram for this test statistic and compute the p-value for the test. Assess the significance of this test: (g) Make a conclusion for this test in full context.
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