Confidence Interval


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?