Question

7. A pharmaceutical believes a newly developed pain reliever will more quickly e d pain to patients after minor surgeries than a standard pain reliever. The standard wy developed pain reliever will more quickly produc andard aan elveris known to bring average of 3.6 minutes with a standard deviation of 2 minutes to test whethe faster than the standard pain reliever 50 patients with minor surseries were given the new data vielded as da yielded a sample mean of 33minutes with standard deviation of 14 minutes th e me sample to indicate, at the level of the the developed p r evede relief more quickly? a. State the null and alternative hypothesis. ni 50 50 HO: ₂ .1.4 X = 3. H : Si 2-3 Specify the level of significance and identify the degrees of freedom if b. needed. c. Sketch the sampling distribution, determine the critical value(s), and determine the rejection region(s). d. Find the standardized test statistic. e. Make a decision to reject or fail to reject the null hypothesis Interpret the decision in the context of the original claim using a complete sentence, At the level of significance,

Answer 1

a. Ho: u = 3.6; HA:N <3.6 b. a = 0.05; df = n - 1 = 50 – 1 = 49; c. Since n > 30, Sampling distribution is Normal with mean = 3.6, 0 2.3 0i = v = 150 = 0.352 Critical value 2er = -1.64; Rejection region : Z< -1.64; I- 3.3 – 3.6 -= -0.852; e. Clearly, test falls in Accept zone, so conclusion is FAIL TO REJECT NULL. f. Interpretation : At the 5% significance level, we dont have suf ficient evidence to conclude that new pain reliever acts more quickly than standard pain reliever. d. Ztest = = 0.352