We are interested in testing the efficacy of a sleeping drug. We have surveyed 10 patients and recorded their hours of sleep under drug and under placebo respectively in the table below. Does the drug increase hours of sieep enough to matter? We have provided you the R file here sieepdrug R that contains the data to get you started. patient 1 drug 6.1 7.0 8.2 7.6 6.5 7.8 6.9 6.7 7.4 5.8 placebo 5.2 7.9 3.9 4.7 5.3 4.8 4.2 6.1 3.8 6.3 4 6 7. 8 9 10 We wil madel the difference of hours of sleep between drug and piacebo for each petient as a normal random variable. Model: X1,..., Xu - N (u, o") (X1, for exampie, wouid be 6.1 - 5.2 = 0.9.) Null hypothesis (Hoku = 0; Alternative hypothesis (Hak u > 0. 1. What would be the power of the hypothesis rest? The probability that the test will conclude that che drug is effective, when in fact it is not The probability thet the test will conclude that the drug is effective, if i is indeed truly effective The probability that the test will conclude that the drug is not effective, when in fact it is The probability that the rest will conclude that the drug is not effective, if it isindeed nat effective 2 If we don't know the variance of the underlying normal distribution (a*, which of the following can you use to test the nul hypothesis? O Fisher exact test O T-cest O Z-test Kolmagrov Smirnov test 3. Since we don't know the true o, we will use the sample variance as an estimate: ? = E (X; - X,). Please enter the value with a precision of two decimal points. 4. What would be an appropriate test statistic T under the null hypothesis, so that T- tn-1 (T-distribution with degrees of freedom n - 1)? 5. What is the p-value? Please enter the value with a precision of three decimal points. p = 6. Can we reject the null hypothesis at a significance level a = 5%? O Yes No