Use the Traditional Method to perform a Hypothesis Test on the following informa

Question

Use the Traditional Method to perform a Hypothesis Test on the following information. Show all steps and drawings needed. Verify with a P-Value. "Generic drugs are less expensive than brand name drugs. A new ointment is being tested for approval. The brand name is known to deliver a mean of 3.5 micrograms of active ingredient per square centimeter of skin area. To test the generic brand seven test patients were applied with the generic ointment and six hours later the recorded micrograms delivered per square centimeter were as follows: 2.6 3.2 2.1 3.0 3.1 2.9 3.7Test the claim that the generic brand is the same is the brand name using a 99% significance level. Use the Traditional Method to perform a Hypothesis Test on the following information. Show all steps and drawings needed. Verify with a P-Value.

Explanation / Answer

n = 7   

= 3.5   

s = 0.5   

x-bar = 2.943   

Hypotheses:   

Ho: = 3.5   

Ha: 3.5   

Decision Rule:   

= 0.01   

Degrees of freedom = 7 - 1 = 6

Lower Critical t- score = -3.70742802

Upper Critical t- score = 3.70742802

Reject Ho if |t| > 3.70742802

Test Statistic:   

SE = s/n = 0.5/7 = 0.188982237

t = (x-bar - )/SE = (2.943 - 3.5)/0.188982236504614 = -2.94737

p- value = 0.025700631   

Decision (in terms of the hypotheses):

Since 2.947366961 < 3.707428 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the generic brand is different from the brand name.

    

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