Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? I

Question

Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study,
researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill.
(a) State the appropriate hypotheses.
(b) Obtain a test statistic and p-value. Interpret the results at a = .01.
(c) Is normality assured?
(d) Is the difference large enough to be important?
(e) What else would medical researchers need to know before prescribing this drug widely?

Explanation / Answer

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(a) Parameters of interest:

"1" = "lovastatin heart attack rate" population mean
"2" = "inactive substitute heart attack rate" population mean

Null Hypothesis H0: (1 - 2) = 0 (no difference between means)

Alternative Hypothesis H1: (1 - 2) < 0 (different means)


(b) Obtain a test statistic and p-value. Interpret the results at alpha = .01

TEST STATISTIC: z1 - z2

z = ()/

= = population proportion = sample proportion
= population standard deviation proportion = SQRT[ * (1 - )/n]


z1 = (approx.) 7.44, z2 = 10.1

z1 - z2 = - 2.66

Probability "P-value" look-up from Standard Normal Table:
P(z1 - z2) = 0.0116001

P-value alpha [0.012 0.01] NOT TRUE!!
Same heart attack rates between Lovastatin and "inactive substitute" to an alpha = 0.01. Cannot reject "Null Hypothesis" H0: (1 - 2) = 0 (no difference between heart attack rate means)

(c) Is normality assured?

For large sample sizes and both > 30, it is not necessary to assume normality by Central Limit Theorem. Utilize Normal Distribution "z" standardized variable.


(d) Is the difference large enough to be important?

Yes! difference is large enough and significant to not reject Null Hypothesis H0: (1 - 2) = 0 (no difference between heart attack rate means)



(e) What else would medical researchers need to know before prescribing this drug widely?

Advise patients lovastatin (a cholesterol-lowering drug) is likely to have same effectivity as "inactive substitute".

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