We can represent the results of the 1 Proportion test in the previous example using a probability distribution plot. Using the binomial distribution, we can show where the results of the study are in relation to the historical figures of 25 percent.
Following on from the previous example, we will use the figures of 92 students in total, out of which 28 smoke regularly. It is not necessary to open the dataset but it may be beneficial to run the previous example to compare the results.
The following steps will use probability distribution plots to generate a binomial distribution for 92 trials and an event probability of 0.25:
92
and for Event probability:, enter the hypothesized probability of 0.25
.28
.The probability distribution plot creates a histogram of the probability density function. For our observed results of 28, we have shaded the area of the distribution above 28. This indicates that we have 0.1399 in the tails of the distribution above 28. As this is a two-sided test and we are checking for a difference, the values of 18 and lower are shaded as well. The area in the distribution below 18 is 0.1383.
Add the two tails together to obtain the P-value of the 1 Proportion test, 0.1383 plus 0.1399 equals 0.2782 - the result of previous example.
For a one-sided test, we can choose to shade just one tail of the distribution.
18.223.195.29