In this video you will learn to compute
confidence intervals for single proportion with summary data using StatCrunch. If a coin is fair the proportion of “heads” the coin will produce over a very long run flips should be 0.5. A coin was flipped 50 times and resulted
in 31 “heads” and 19 “tails, so for this video the statistical question I’m going to
investigate is: ‘Do the 50 outcomes in the short
run of flips in this dataset suggest the coin is unfair?”
To compute the appropriate confidence interval, Under the “stat” menu, choose “proportion stats”, “one sample”, “with summary”, since I don’t have the actual data for
each trial in the data table. In StatCrunch, a success is used to define the outcome of
interest. In this case we consider a “heads” result to be a success, so set the number of successes to be 31 and the number of observations to be
50. Under “perform” I’ll choose a confidence interval. By
default StatCrunch assigns a value 0.95 per the level which will produce a
95 percent confidence interval for the population proportion. Changing this value to 0.99 will produce a 99 percent confidence
interval For this example I’ll leave it at 0.95 and click compute. The results show a 95
percent confidence interval for the long-run proportion of “heads” where “L. Limit” is the lower limit and “U. Limit” is the upper limit of the confidence interval. By default StatCrunch uses the Standard-Wald normal approximation for calculating confidence intervals.
Instead we can use the alternative Agresti-Coull method. To do so under “options” choose “edit”. Under “method”, I’ll choose “Agresti-Coull” and then click
compute. Now the results show a new confidence interval.