Omar Lewis
Binomial Probability Experiment
The chosen binomial experiment is to ask 100 college students about their age. For the experiment to me deemed successful, the age group has to be between 18 years and 30 years (Illowsky, Dean, & Illowsky, 2017). It is estimated there is 60% success rate.
The results of the experiments are as follows:
| Students | Age | Success or Failure |
| 1 | 21 | Success |
| 2 | 37 | Failure |
| 3 | 18 | Success |
| 4 | 36 | Failure |
| 5 | 44 | Failure |
| 6 | 31 | Failure |
| 7 | 42 | Failure |
| 8 | 30 | Failure |
| 9 | 34 | Failure |
| 10 | 21 | Success |
| 11 | 26 | Success |
| 12 | 30 | Failure |
| 13 | 25 | Success |
| 14 | 35 | Failure |
| 15 | 35 | Failure |
| 16 | 44 | Failure |
| 17 | 28 | Success |
| 18 | 27 | Success |
| 19 | 19 | Success |
| 20 | 22 | Success |
| 21 | 35 | Failure |
| 22 | 43 | Failure |
| 23 | 38 | Failure |
| 24 | 23 | Success |
| 25 | 26 | Success |
| 26 | 39 | Failure |
| 27 | 31 | Failure |
| 28 | 21 | Success |
| 29 | 23 | Success |
| 30 | 35 | Failure |
| 31 | 32 | Failure |
| 32 | 34 | Failure |
| 33 | 33 | Failure |
| 34 | 25 | Success |
| 35 | 43 | Failure |
| 36 | 27 | Success |
| 37 | 27 | Success |
| 38 | 31 | Failure |
| 39 | 38 | Failure |
| 40 | 34 | Failure |
| 41 | 41 | Failure |
| 42 | 18 | Success |
| 43 | 22 | Success |
| 44 | 17 | Success |
| 45 | 30 | Failure |
| 46 | 19 | Success |
| 47 | 26 | Success |
| 48 | 33 | Failure |
| 49 | 42 | Failure |
| 50 | 42 | Failure |
| Success | 21 | |
| Failure | 29 |
From the results of the above test, the probability of success was 21/50= .42= 42%
The reason why there 42% success rate is that there are many support staff in colleges whose age varies greatly. It is also possible to find old students (Illowsky, Dean, & Illowsky, 2017).
Instructions for Project 3 Assignment:
Use the results of Project #2. Recall that you performed a binomial probability experiment 50 times. In Project #3, you will calculate a 90% confidence interval, a 95% confidence interval, and a 99% confidence interval for the true probability of success
Hints: Suppose, you guessed that there would be 28 successes i.e. p = .56 or 56%. After the actual experiment was done, you got 24 successes which gives a result of p = .48 or 48% and q = .52 or 52%. Therefore, the actual probability deviates from the guess 56%. Use the computed values of p and q when computing the confidence intervals (not your guess.)
Write a paragraph to explain your results. State you guess and the computed probability of success from Project #2. Show the formulas you used to compute the 90%, 95% and the 99% confidence intervals, and state each confidence interval. Explain if any of these intervals contain your original guess. Do you consider your original guess accurate or inaccurate?
