Population Mean Inference

Data Summary

Variable Sample Size Mean Sample Std Dev
MPG (Subcompact) 22 41.3318 8.46097
MPG (Compact) 16 36.1313 8.62428

Test of Hypothesis: t-Test
MPG (Subcompact) - MPG (Compact)

Alternative Hypothesis Ha: Difference of means 'MPG (Subcompact) - MPG (Compact)' is greater than 0
5% upper critical value in units of data = 4.73138
Equal population variances was assumed.

Difference of Means Std Error Obs t Stat DF 5% t-Upper Critical P-value
5.20057 2.80246 1.85572 36 1.6883 0.0358476

Test is significant at 5% level.

P-value Graph: t-Test

Null density (in units of data): Student t; mean = 0, scale = 2.8025, df = 36
Alternative Hypothesis Ha: Difference of means 'MPG (Subcompact) - MPG (Compact)' is greater than 0
Assumed equal population variances; pooled variance was used.

The title of the graph is P-value Graph: t-Test , The graph shows the distribution of Diff. of Sample Means , Obs Diff. of Sample Means = 5.2006 , P-Value = 0.035848

Test of Hypothesis: z-Test
MPG (Subcompact) - MPG (Compact)

Alternative Hypothesis Ha: Difference of means 'MPG (Subcompact) - MPG (Compact)' is greater than 0
5% upper critical value in units of data = 4.623953

Difference of Means Std Error Obs z Stat 5% z-Upper Critical P-Value
5.20057 2.81116 1.84997 1.64485 0.032159

Test is significant at 5% level.

P-value Graph: z-Test

Null density (in units of data): Normal; mean = 0 , sd = 2.8112
Alternative Hypothesis Ha: Difference of means 'MPG (Subcompact) - MPG (Compact)' is greater than 0

The title of the graph is P-value Graph: z-Test , The graph shows the distribution of Diff. of Sample Means , Obs Diff. of Sample Means = 5.2006 , P-Value = 0.032159

Test of Hypothesis: Bootstrap Unscaled Difference of Means
MPG (Subcompact) - MPG (Compact)

Alternative Hypothesis Ha: Difference of means 'MPG (Subcompact) - MPG (Compact)' is greater than 0
Number of replications = 10000; Random generator seed = 100

Diff Obs Sample Means Mean Bootstrap Diff SD Bootstrap Diff 5% Upper Critical Value P-Value
5.20057 -0.00948922 2.70779 4.40057 0.0235976

Test is significant at 5% level.

Distribution of Bootstrap Replicates: Sample Mean
MPG (Subcompact) - MPG (Compact)

Number of replications = 10000, Random generator seed = 100

The title of the graph is Alternative Hypothesis Ha: Mean of 'MPG (Subcompact)' is greater than Mean of 'MPG (Compact)' Distribution of bootstrap replications of difference of sample means (unscaled) , The graph shows the distribution of bootstrap replicates of MPG (Subcompact) - MPG (Compact) , Obs. Diff. of Sample Means = 5.200568 , P-Value = 0.02359764 , Critical boundary for alpha = 5% , Critical value = 4.400568

Test of Hypothesis: Permutation Unscaled Difference of Means
MPG (Subcompact) - MPG (Compact)

Alternative Hypothesis Ha: Difference of means 'MPG (Subcompact) - MPG (Compact)' is greater than 0
Number of replications = 10000; Random generator seed = 100

Diff Obs Sample Means Mean Permutation Diff SD Permutation Diff 5% Upper Critical Value P-Value
5.20057 -0.00930998 2.89499 4.69318 0.0349965

Test is significant at 5% level.

Distribution of Permutation Replicates: Sample Mean
MPG (Subcompact) - MPG (Compact)

Number of replications = 10000, Random generator seed = 100

The title of the graph is Alternative Hypothesis Ha: Mean of 'MPG (Subcompact)' is greater than Mean of 'MPG (Compact)' Distribution of permutation replications of difference of sample means (unscaled) , The graph shows the distribution of Permutation-test MPG (Subcompact) - MPG (Compact) , Obs. Diff. of Sample Means = 5.200568 , P-Value = 0.0349965 , Critical boundary for alpha = 5% , Critical value = 4.693182