Econometrics. For the following problem state (i) all relevant null and alternat
ID: 3217065 • Letter: E
Question
Econometrics. For the following problem state (i) all relevant null and alternative hypothesis (ii) the relevant parameters of the sampling distribution(s), (iii) whether the sample distribution is distributed normally, as a t distribution, F distribution, or Chi square (iv) whether this is a one-tailed or two-tailed test and v) what significance level you use and why. Then test the null hypothesis and state your conclusion(s). Show every step of every calculation or inference upon which you based your answer.
Recently your uncle went for a physical. The doctor told him that his cholesterol was extremely low and that he needs to reduce it significantly or face dire consequences. The doctor provides your uncle with a choice of two medications. Pill A reduces cholesterol on average 40 points in a sample of 9, with a standard deviation of 66 points. Pill B reduces cholesterol in a similar sized sample on average 3 points with a standard deviation of 0.03 points. Assess which pill has more statistically significant impact and issue a recommendation to your uncle as to which pill he should take.
Some Information About Cholesterol
Total Cholesterol Level Category
Less than 200mg/dL Desirable
200-239 mg/dL Borderline high
240 mg/dL and above High
Explanation / Answer
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (9-1)*66^2+(9-1)*0.03^2/8+8
= 34848+0.0072
=2178
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(40-3)-0/2178(1/9+1/9)
=37/22
=1.68
tCRIT at 0.025 on each side (0.05/2) is 2.1199 and hence cannot reject the null hypothesis.
P.S:- I have calculated the above taking 66 as std.dev. However, a std.dev can never be greater than mean. I suppose, it should be 6.6. Whatever be the case, just substitute the values in the above formula and you would get the answer.
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