Saltfree diets are often prescribed to people with high bloo

Salt-free diets are often prescribed to people with high blood pressure. The following data were obtained as part of a study to measure the effect on diastolic blood pressure as a result of following a salt-free diet for two weeks. Assume the diastolic reading differences are normally distributed in the population. Does a salt-free diet reduce diastolic blood pressure? Participants were randomly selected for the study.

What are the null and the alternative hypotheses?

Are the assumptions necessary for inference met?

Perform the appropriate test including the formula that you used, the calculated value of the t-statistic, and the t-critical you compared to your t-statistic.

State your conclusion.

Solution

Let group 2 = after results
group 1 = before results

Let ud = u2 - u1.              

A)

Formulating the null and alternative hypotheses,              
              
Ho:   ud   >=   0  
Ha:   ud   <   0   [ANSWER]

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B)

Yes, as the reading differences are normally distributed, and the sample is randomly selected.

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c)

At level of significance =    0.05          
As we can see, this is a    left   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    1.975225342          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.698347617          
              
Calculating the mean of the differences (third column):              
              
XD =    -1.625          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -2.32692138          
              
As df = n - 1 =    7          
              
Then the critical value of t is              
              
tcrit =    -   2.364624252      
              
As t > -2.365, we   WE FAIL TO REJECT THE NULL HYPOTHESIS.          

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d)

There is no significant evidence at 0.05 level that the salt-free diet reduce diastolic blood pressure. [CONCLUSION]