In the development of new drugs for the treatment of anxiety

In the development of new drugs for the treatment of anxiety, it is important to check the drug\'s effects on various motor functions, one of which is driving. The Confab Pharmaceutical Company is testing four different tranquilizing drugs for their effects on driving skill. Subjects take a simulated driving test, and their scores reflect their error. The more severe errors lead to higher scores. The results of these tests produced in the following table.

Drug 1: ni=4 xj=246 si=8.37
Drug 2: ni=4 xi=273 si=6.06
Drug 3: ni=5 xi=230 si=10.42
Drug 4: ni=5 xi=244 si=6.63

Calculate the overall sample mean, MSE, MSTR, and appropriate test statistic.
A. 247, 66.4625, 1399.3333, Ftest=21.0545
B. 248.25, 66.4625, 1408.7083, Ftest=21.1955
C. 248.25, 7.9636, 1408.7083, Ftest=176.8940
D. 247, 7.9636, 1399.3333, Ftest=175.7162

At 5% level of significance, do the four drugs affect driving skill differently?
A. Fcrit=3.34 < Ftest. Failed to reject the null hypothesis. The four drugs have different affect on driving skill.
B. Fcrit=3.34 < Ftest. Reject the null hypothesis. The four drugs have same affect on driving skill.
C. Fcrit=3.34 < Ftest. Failed to reject the null hypothesis. The four drugs have same affect on driving skill.
D. Fcrit=3.34 < Ftest. Reject the null hypothesis. The four drugs have different affect on driving skill.

Thanks in advance, not sure why out of 30 questions, I\'m only having issues with this one.

Solution

As

grand mean = Sum(ni Xi) / Sum(ni)

Thus,

grand mean = 247

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As

MSE = Sum ((ni - 1) si^2) / [Sum (ni) - k]

where k = 4, the number of groups.

Then,

MSE = 66.46247857

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Thus, from these two choices alone, we know that the answer is OPTION A: 247, 66.4625, 1399.3333, Ftest=21.0545 [ANSWER, OPTION A]

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CONCLUSION:

D. Fcrit=3.34 < Ftest. Reject the null hypothesis. The four drugs have different affect on driving skill. [ANSWER, OPTION D]