Question

3. A health researcher in a hospital believes that the mean cholesterol level for certain male population aged-50 is 241. An investigator wishes to examine whether the cholesterol levels are significantly reduced by modifying diet. A random sample of 12 patients agrees to participate in the study and follow the modified diet for 3 months. After 3 months, their cholesterol levels are measured. The mean cholesterol level in the sample is 235 with a standard deviation of 12.5. Based on these data, is there statistical evidence that the modified diet reduces cholesterol? Use a= 0.05 (a) State the null and alternative hypothesis for this test (b) Calculate the test statistic and the critical value. (c) Graph your curve and mark the critical value(s) and rejection region (d) Based on the test statistic and the critical value, state your conclusion (e) Construct a 90% confidence interval estimate for the true average cholesterol level of male aged-50

Answer 1

Given that l=241, n = 12, x=235, S = 12.5, 2=0.05 - (a) Noll hypother's (Ho): l=241 Alternative hypothesis (Ha): u<241 (claim (6) Test statistic: t= x-1 = 235-241 -1.6628 - Sun 12.5/12 t = -1.66 critical value: At 2=0.05 l.o.s, df = 11 Cleft tailed) doc.v=-2.201 2=0.05 df-11 Reje region / Accept echon - 2- 201 (d) tal- ter i.e., -1.66 -2.201 so fail to reject to a At a = 0.05 1.0.s there is no statistical evidence that the modified diet reduces cholesterol

(e) १० at a = 0.10 1.015, df = 11,t-cir= 1.796 235+ (11१6) 12.5 235 16.4808 (228,5192 , 2 ५। . ५806) - १०/- 228.52 - 0 241.48