One Population Proportion Inference

Data Summary

Counts and Percentages: volunteer

- yes no Total
Count 597 824 1421
Percentage 42.01267 57.98733 100

Test of Hypothesis: volunteer
Method: Binomial Exact Test

Alternative Hypothesis Ha: Proportion of 'yes' is less than 0.45

Sample Size No. of Successes Sample Proportion P-Value BFB
1421 597 0.420127 0.0125125 6.71096

  • Test is significant at 5% level.
  • Bayes Factor Bound (BFB): The data imply the odds in favor of
    the alternative hypothesis is at most 6.71 to 1, relative to the null hypothesis.

P-Value Graph: volunteer
Method: Exact Binomial Test

Null Distribution: Binomial; n = 1421, p = 0.45
Alternative Hypothesis Ha: Proportion of 'yes' is less than 0.45

, The graph shows the distribution of Number of Successes , Observed Value = 597 , P - Value == P(X <= 597) , P - Value == 0.01251

Test of Hypothesis: volunteer
Method: Large Sample z Test (Using p0)

Alternative Hypothesis Ha: Proportion of 'yes' is less than 0.45

Sample Proportion Std Error Standardized Obs Stat 5% z-Lower Critical P-Value BFB
0.420127 0.0131975 -2.26357 -1.64485 0.0118004 7.02202

  • Test is significant at 5% level.
  • Bayes Factor Bound (BFB): The data imply the odds in favor of
    the alternative hypothesis is at most 7.02 to 1, relative to the null hypothesis.

P-value Graph: Large Sample z (Using p0)

Null density (in units of data): Normal; mean = 0.45 , sd = 0.013197
Alternative Hypothesis Ha: Proportion of 'yes' is less than 0.45

The title of the graph is P-value Graph: Large Sample z (Using p0) , The graph shows the distribution of Proportion of yes , Observed Sample Prop = 0.42013 , P-value = 0.0118/div>