Question

2. Salt-free diets are often prescribed to people with high blood pressure. The following data values were obtained from an experiment designed to estimate the reduction in diastolic blood pres- sure as a result of consuming a salt-free diet for 2 weeks. Assume diastolic readings to be normally distributed.

   (a) Calculate a 90% confidence interval for the mean reduction.
   (b) Is there evidence that diastolic blood pressure is reduced by having salt-free diets, use α = 0.05.

Patients A. B. C.    D. E. F. G. H

Before. 93.   106 87 92 102 95 88 110

After. 92. 102 89 92 101 96 88 105

Answer 1

(a) From the Data: = -1 and Sd = 2.3905

= 0.10, the degrees of freedom = n – 1 = 7

The critical value = 1.895

The Confidence interval is given by ME

The Lower Limit = -1 – 1.602 = -2.602

The Upper Limit = -1 + 1.602 = 0.602

The 90% Confidence interval is (-2.602, 0.602)

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(b) The Hypothesis:

H0: = 0 : The test preparation has no effect on the scores.

Ha: < 0: The test preparation has an effect on the scores.

This is a left tailed test

The Test Statistic: Since sample size is small, and population std. deviation is unknown, we use the students t test.

The p value: (Left tailed) at t = -1.18, degrees of freedom = n -1 = 8 - 1 = 7 is p value = 0.1383

The Critical values: (Left Tail) for = 0.05, df = 7 is -1.895

The Decision Rule:   If t observed is < -t critical, Then reject H0.

Also if P value is < , Then Reject H0.

The Decision:   Since t observed (-1.18) is > t critical (-1.895), We fail to Reject H0.

Also since P value (0.1383) is > (0.05) , We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to conclude that the diastolic blood pressure is reduced by having salt free diets.

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Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)².

#	Difference	Mean	(X-Mean)2
1	-1	-1	0
2	-4	-1	9
3	2	-1	9
4	0	-1	1
5	-1	-1	0
6	1	-1	4
7	0	-1	1
8	-5	-1	16

n	8
Sum	-8
Mean	-1
SS	40
Variance	5.7143
Std Dev	2.3905