One Population Mean Inference

Data Summary

Variable Sample Size Mean Sample Std Dev
Miles Per Gallon 82 33.7817 10.0046

Test of Hypothesis: t-Test
Miles Per Gallon

Alternative Hypothesis Ha: Mean of 'Miles Per Gallon' is greater than 32
5% upper critical value in units of data = 33.8383

Sample Mean Std Error Obs t Stat DF 5% t-Upper Critical P-value
33.7817 1.10482 1.61266 81 1.66388 0.0553538

Test is not significant at 5% level.

P-value Graph: t-Test

Null density (in units of data): Student t; mean = 32, scale = 1.1048, df = 81
Alternative Hypothesis Ha: Mean of 'Miles Per Gallon' is greater than 32

The title of the graph is P-value Graph: t-Test , The graph shows the distribution of Sample Mean , Obs Sample Mean = 33.782 , P-Value = 0.055354

Test of Hypothesis: z-Test
Miles Per Gallon

Alternative Hypothesis Ha: Mean of 'Miles Per Gallon' is greater than 32
5% upper critical value in units of data = 33.81727

Sample Mean Std Error Obs z Stat 5% z-Upper Critical P-Value
33.7817 1.10482 1.61266 1.64485 0.053409

Test is not significant at 5% level.

P-value Graph: z-Test

Null density (in units of data): Normal; mean = 32 , sd = 1.1048
Alternative Hypothesis Ha: Mean of 'Miles Per Gallon' is greater than 32

The title of the graph is P-value Graph: z-Test , The graph shows the distribution of Sample Mean , Obs Sample Mean = 33.782 , P-Value = 0.053409

Test of Hypothesis: Bootstrap (Unscaled Sample Mean)
Miles Per Gallon

Alternative Hypothesis Ha: Mean of 'Miles Per Gallon' is greater than 32
Number of replications = 10000; Random generator seed = 100

Observed Sample Mean Bootstrap Mean Bootstrap SD 5% Upper Critical Value P-Value
33.7817 32.0074 1.09117 33.8402 0.0564944

Test is not significant at 5% level.

Distribution of Bootstrap Replicates: Sample Mean
Miles Per Gallon

Number of replications = 10000, Random generator seed = 100

The title of the graph is Alternative Hypothesis Ha: Mean of 'Miles Per Gallon' is greater than 32 Distribution of bootstrap replications of sample mean (unscaled) , The graph shows the distribution of bootstrap replicates of Miles Per Gallon , Observed Sample Mean = 33.78171 , P-Value = 0.05649435 , Critical boundary for alpha = 5% , Critical value = 33.84024