Researchers are interested in testing the efficacy (effectiveness) of a drug to

Question

Researchers are interested in testing the efficacy (effectiveness) of a drug to reduce blood pressure. We will assume that the change in blood pressure is measured as baseline blood pressure (before taking the drug) MINUS blood pressure after taking the drug for 1 month. Suppose that this variable is normally distributed with = 14. A random sample of 25 men aged 50-65 is randomly selected. Their baseline blood pressure is measured and then they are given the drug. After a month their blood pressure is measured again. From this, the change in blood pressure is calculated for each subject. The sample mean of the change in blood pressure is found to be 4.

(a) What hypotheses should be used to test the claim?

H0: = 0 and Ha: > 0We can't answer this question because we aren't given the null value in the statement of the problem.     H0: = 4 and Ha: >4H0: = 0 and Ha: < 0H0: X = 0 and Ha: x > 0

(c) Assume the conditions are met, what is the p-value of the test?


(d) Assume = 0.05. Should you reject or fail to reject?

RejectFail to reject     

(e) Complete the conclusion statement below. For the first blank your choices are: provides, does not provide.

Explanation / Answer

We will assume that the change in blood pressure is measured as baseline blood pressure (before taking the drug) MINUS blood pressure after taking the drug for 1 month.

As blood pressure is assumed to be redcued, then this difference is positive, so this is a right tailed test.

a)

OPTION A: H0: = 0 and Ha: > 0 [ANSWER]

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C)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   0  
Ha:    u   >   0  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    4          
uo = hypothesized mean =    0          
n = sample size =    25          
s = standard deviation =    14          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.428571429          
              
Also, the p value is              
              
p =    0.076563726   [ANSWER]      

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D)

As P > 0.05, WE FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER]

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E)

Hence, our sample DOES NOT PROVIDE sufficient evidence of a significant reduction in blood pressure at 0.05 level. [CONCLUSION]

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