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3. [10 marks] A random sample of n = 100 adults suffering from anxiety were administered the recommended dosage of a commonly prescribed drug; of these, 70 experienced relief after a two-week period. (a) Verify that the sample size is large enough for a large sample confidence interval for p. (b) Construct a symmetric 95% confidence interval for the true proportion of adults who experience relief from anxiety with this drug. Express your final answer to at least two decimal places. (c) The drug manufacturer claims that more than 60% of individuals suffering from anxiety will experience relief after taking the recommended dosage for two weeks. Do the data given above provide evidence at the 5% level that this claim is valid; that is, that the true proportion of individuals reporting relief from anxiety after two weeks of the recommended dosage is more than 60%? Include a check that the conditions for inference are met. Normality check: Ho: Ha: Level of Significance: Observed test statistic (to 2 decimal places): p-value: Decision: Conclusion: (d) Indicate the meaning of a Type I Error for the hypothesis test in (c), and give, with appropriate justification, the probability (if it is known) of making such a mistake