SamplingDistributions and Confidence Intervals
SamplingDistributions and Confidence Intervals
Thedata analyzed here is the number of children in living with HIV andare below the age of 10 in various regions in Africa. The 95% and 90%confidence interval for the sample of 100 regions are as shown below.
95%Confidence Interval
TTEST
/TESTVAL=0
/MISSING=ANALYSIS
/VARIABLES=CHILDREN
/CRITERIA=CI(.95).
OneSample Statistics 

N 
Mean 
Std. Deviation 
Std. Error Mean 

Children living with HIV below the age of 10 
100 
84.2591 
16.22828 
1.62283 
OneSample Test 

Test Value = 0 

t 
df 
Sig. (2tailed) 
Mean Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Children living with HIV below the age of 10 
51.921 
99 
.000 
84.25910 
81.0391 
87.4791 
90%Confidence Interval
TTEST
/TESTVAL=0
/MISSING=ANALYSIS
/VARIABLES=CHILDREN
/CRITERIA=CI(.90).
OneSample Statistics 

N 
Mean 
Std. Deviation 
Std. Error Mean 

Children living with HIV below the age of 10 
100 
84.2591 
16.22828 
1.62283 
OneSample Test 

Test Value = 0 

t 
df 
Sig. (2tailed) 
Mean Difference 
90% Confidence Interval of the Difference 

Lower 
Upper 

Children living with HIV below the age of 10 
51.921 
99 
.000 
84.25910 
81.5646 
86.9536 
Fromthe above results, it is evident that the higher the confidencepercentage (95%), the higher the interval (81.0487.48). Similarly,the lower the confidence interval percentage, the lower the intervalbetween the means (81.5685.95). The 95% and 90% confidence intervalresults for the sample of 400 are as shown below.
95%Confidence Interval
OneSample Statistics 

N 
Mean 
Std. Deviation 
Std. Error Mean 

Children living with HIV below the age of 10 
400 
83.8119 
16.38943 
.81947 
OneSample Test 

Test Value = 0 

t 
df 
Sig. (2tailed) 
Mean Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Children living with HIV below the age of 10 
102.276 
399 
.000 
83.81187 
82.2009 
85.4229 
90%Confidence Interval
OneSample Statistics 

N 
Mean 
Std. Deviation 
Std. Error Mean 

Children living with HIV below the age of 10 
400 
83.8119 
16.38943 
.81947 
OneSample Test 

Test Value = 0 

t 
df 
Sig. (2tailed) 
Mean Difference 
90% Confidence Interval of the Difference 

Lower 
Upper 

Children living with HIV below the age of 10 
102.276 
399 
.000 
83.81187 
82.4608 
85.1629 
Fromthe above results, it is clear that higher sample value makes theconfidence intervals to be almost the same for the 95% and 90% hencemaking the data to have less errors and hence have high level ofreliability and authenticity. A larger sample also have the effect ofreducing the intervals within the means in line with the confidenceintervals. Larger deviations from the means is experienced with thelow sample amounts.