Population Mean Inference

Data Summary

Variable Sample Size Mean Sample Std Dev
Initial.Weight 68 136.074 24.3711
Terminal.Weight 68 137.985 24.6101
[Initial.Weight - Terminal.Weight] 68 -1.91176 2.12824

Statistics for the difference [Initial.Weight - Terminal.Weight] is based on differences of observed pairs of data.

Test of Hypothesis: Paired t-Test
[Initial.Weight - Terminal.Weight]

Alternative Hypothesis Ha: Mean of paired differences '[Initial.Weight - Terminal.Weight]' is less than 0
5% lower critical value in units of data = -0.4304678
Differences of pairs were used.

Mean of Paired Diff Std Error Obs t Stat DF 5% t-Lower Critical P-value
-1.91176 0.258087 -7.40744 67 -1.66792 1.40637e-10

Test is significant at 5% level.

P-value Graph: Paired t-Test

Null density (in units of data): Student t; mean = 0, scale = 0.25809, df = 67
Alternative Hypothesis Ha: Mean of differences '[Initial.Weight - Terminal.Weight]' is less than 0

The title of the graph is P-value Graph: Paired t-Test , The graph shows the distribution of Diff. of Sample Means , Obs Diff. of Sample Means = -1.9118 , P-Value = 1.4064e-10

Test of Hypothesis: Paired z-Test
[Initial.Weight - Terminal.Weight]

Alternative Hypothesis Ha: Mean of paired differences '[Initial.Weight - Terminal.Weight]' is less than 0
5% lower critical value in units of data = -0.4245156
Differences of pairs were used.

Mean of Paired Diff Std Error Obs z Stat 5% z-Lower Critical P-Value
-1.91176 0.258087 -7.40744 -1.64485 6.43816e-14

Test is significant at 5% level.

P-value Graph: Paired z-Test

Null density (in units of data): Normal; mean = 0 , sd = 0.25809
Alternative Hypothesis Ha: Mean of differences '[Initial.Weight - Terminal.Weight]' is less than 0

The title of the graph is P-value Graph: Paired z-Test , The graph shows the distribution of Mean of Paired Diffs , Obs Mean of Paired Diffs = -1.9118 , P-Value = 6.4382e-14

Test of Hypothesis: Bootstrap (Unscaled Mean of Paired Differences)
Initial.Weight - Terminal.Weight

Alternative Hypothesis Ha: Mean of differences 'Initial.Weight - Terminal.Weight' is less than 0
Number of replications = 10000; Random generator seed = 100

Mean Obs Paired Diffs Mean Bootstrap Paired Diff SD Bootstrap Paired Diff 5% Lower Critical Value P-Value
-1.91176 0.00226595 0.258497 -0.426471 9.999e-05

Test is significant at 5% level.

Distribution of Bootstrap Replicates: Mean of Paired Differences
Initial.Weight - Terminal.Weight

Number of replications = 10000, Random generator seed = 100

The title of the graph is Alternative Hypothesis Ha: Mean of 'Initial.Weight' is less than Mean of 'Terminal.Weight' Distribution of simulated paired differences (Bootstrap Unscaled) , The graph shows the distribution of bootstrap replicates of Initial.Weight - Terminal.Weight , Obs. Diff. of Sample Means = -1.911765 , P-Value = 9.999e-05 , Critical boundary for alpha = 5% , Critical value = -0.4264706

Test of Hypothesis: Permutation (Unscaled Mean of Paired Differences)
Initial.Weight - Terminal.Weight

Alternative Hypothesis Ha: Mean of differences 'Initial.Weight - Terminal.Weight' is less than 0
Number of replications = 10000; Random generator seed = 100

Mean Obs Paired Diffs Mean Permutation Paired Diff SD Permutation Paired Diff 5% Lower Critical Value P-Value
-1.91176 -0.00254975 0.344153 -0.558824 9.999e-05

Test is significant at 5% level.

Distribution of Permutation Replicates: Mean of Paired Differences
Initial.Weight - Terminal.Weight

Number of replications = 10000, Random generator seed = 100

The title of the graph is Alternative Hypothesis Ha: Mean of 'Initial.Weight' is less than Mean of 'Terminal.Weight' Distribution of replications of difference of permuted pairs (unscaled) , The graph shows the distribution of Permutation-test Initial.Weight - Terminal.Weight , Obs. Diff. of Sample Means = -1.911765 , P-Value = 9.999e-05 , Critical boundary for alpha = 5% , Critical value = -0.5588235