Use the following data set to perform the t-test and determine p-values: The dat
ID: 3261331 • Letter: U
Question
Use the following data set to perform the t-test and determine p-values:
The data studies the effect of dietary calcium on blood pressure. In the experiment, one group of black male adults received calcium supplements for 12 weeks. A control group of black male adults was given placebos for 12 weeks. Earlier tests indicated that calcium could be more effective in the black population. The data are seated systolic blood pressure at the beginning and end of the 12 weeks measured in mm Hg. The data include the decrease after 12 weeks (a negative value indicates an increase).
If you choose to use the table for calculating the p value range, please also report what you calculated for t (or for F)!!!!!! Data from Lyle et al., JAMA 257:1772-1776 (1987)
Calcium Group
Begin End Decrease
107 100 7
110 114 -4
123 105 18
129 112 17
112 115 -3
111 116 -5
107 106 1
112 102 10
136 125 11
102 104 -2
Placebo Group
Begin End Decrease
123 124 -1
109 97 12
112 113 -1
102 105 -3
98 95 3
114 119 -5
119 114 5
112 114 -2
110 121 -11
117 118 -1
130 133 -3
C. Treat the two groups (calcium and placebo) as independent samples, equal variances. Look only at the decrease columns (you are now comparing the calcium decrease column to the placebo decrease column). Perform a test to determine the p-value for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease.
D. Treat the two groups as independent samples, unequal variances. Look only at the decrease columns (calcium vs. placebo). Perform a test to determine the p-value for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease.
E. Do a two-sided t-test to compare the sample groups. Look at the Begin column for calcium and the Begin column for placebo. Report the p-value. Based on that p-value, do you have any reason to believe that the sample groups were significantly different headed into the experiment?
DATA SET BELOW:
GROUP BEGIN END DECREASE 1 107 100 7 1 110 114 -4 1 123 105 18 1 129 112 17 1 112 115 -3 1 111 116 -5 1 107 106 1 1 112 102 10 1 136 125 11 1 102 104 -2 0 123 124 -1 0 109 97 12 0 112 113 -1 0 102 105 -3 0 98 95 3 0 114 119 -5 0 119 114 5 0 112 114 -2 0 110 121 -11 0 117 118 -1 0 130 133 -3Explanation / Answer
C. Null hypothesis – H0 : 1 = 2
Alternative hypothesis – H1 : 1 > 2 ,
where 1 and 2 are the means of calcium decrease values and placebo decrease values, respectively.
Here, variances of calcium decrease values and placebo decrease values are equal.
P-value = 0.04814.
Here, p – value < 0.05, thus we reject null hypothesis and conclude that calcium is more effective than placebo in the black population.
95 percent confidence interval : (0.06682212,Infinity)
R codes :
x=c(7,-4,18,17,-3,-5,1,10,11,-2)
y=c(-1,12,-1,-3,3,-5,5,-2,-11,-1,-3)
t.test(x,y,alternative = "g",mu=0,paired=F,var.equal=TRUE,conf.level=0.95)
D. Null hypothesis – H0 : 1 = 2
Alternative hypothesis – H1 : 1 > 2.
Here, variances of calcium decrease values and placebo decrease values are unequal.
P-value = 0.05293.
Here, p – value > 0.05, thus we accept null hypothesis and conclude that calcium is not more effective than placebo in the black population.
95 percent confidence interval : (-0.105456 ,Infinity)
R codes :
t.test(x,y,alternative = "g",mu=0,paired=F,var.equal=F,conf.level=0.95)
E. i) Variances considered equal : p – value = 0.7116
ii) Variances considered unequal : p-value = 0.7144
In both the cases, p-value > 0.05, thus we accept null hypothesis and conclude that the sample groups are not significantly different headed into the experiment.
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