a) what test is apropriate for determining if there was a reduction in sodium in

Question

a) what test is apropriate for determining if there was a reduction in sodium intake?

b) what are the appropriate null and alternate hypotheses to test if dietary conseling is effective in reducing sodium intake (as measured by sodium excretion given in the table)?

c) Condict the test from part a. Report a p-value that is appropriate for the alternate hypotheses in the table.

d) Construct a 95% confidence interval for the mean difference obtained from the information in the table.

e) Combinnb information from part c and d state your conclusion for a significance level a = 0.025

Week 0 Week 1

7.85 9.59

12.03 30.50

21.84 4.55

13.94 20.78

16.68 11.69

41.78 32.51

14.97 4.46

12.07 11.95

Explanation / Answer

a)

The same participants are for week 0 and week 1, so it is a [[PAIRED T TEST]]. [ANSWER]

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b)

Let

x2 = week 1 values
x1 = week 2 values

ud = u(x2-x1).

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

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c)

At level of significance =    0.025          

As we can see, this is a    left   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    9.005701687          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    3.183996366          
              
Calculating the mean of the differences (third column):              
              
XD =    -1.89125          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -0.593986231          
              
As df = n - 1 =    7          
              
              
Also, using p values,              
              
p =        0.285604888   [ANSWER, P VALUE]  
              
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d)

For the   0.95   confidence level,      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
t(alpha/2) =    2.364624252          
              
lower bound = [X2 - X1] - t(alpha/2) * sD =    -9.420205024          
upper bound = [X2 - X1] + t(alpha/2) * sD =    5.637705024          
              
Thus, the confidence interval is              
              
( -5.637705024,   9.420205024 ) [ANSWER]

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e)

As P > 0.025, and the interval in d) includes, 0, then we fail to reject Ho.

There is no significant evidence that there was a reduction in sodium intake at 0.025 level. [CONCLUSION]

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