A1.4
C I FOR THE DIFFERENCE OF POPULATION PROPORTIONS
The question:
Independent Samples from two major league teams were selected from the American League. Each team was asked to comment on their opinion relating to the coaching staff’s ability to resolve conflicts within the organization. Fifty players were selected from the first sample consisting of seniority years between 5 – 10 years in the league regardless of team of which 72% indicated they felt the staff was effective when resolving disputes within the organization. The second group consisted of 60 players whose seniority in the league was less then 5 years of which 80% indicated they felt the coaching staff was effective when resolving disputes within the organization. Find the 90% confidence interval for the difference in proportions between these two age groups. Interpret the interval in words.
The question stem: What are they asking you to determine?
Find the 95% confidence interval of the mean for all females spent studying. Interpret the interval in words.
What are you given?
Independent Samples from two major league teams were selected from the American League. Each team was asked to comment on their opinion relating to the coaching staff’s ability to resolve conflicts within the organization. Fifty players were selected from the first sample consisting of seniority years between 5 – 10 years in the league regardless of team of which 72% indicated they felt the staff was effective when resolving disputes within the organization. The second group consisted of 60 players whose seniority in the league was less then 5 years of which 80% indicated they felt the coaching staff was effective when resolving disputes within the organization. Find the 90% confidence interval for the difference in proportions between these two age groups. Interpret the interval in words.
Identify your variables:
*Independent samples
*Note: In these types of questions you must check the assumptions first and make sure that both np >5 & nq >5
In this case the total n = 110
**90% confidence in the results, which means critical value is 1.645
The formula: for a Two Proportion ZInterval (2-PropZInterval)
Question type: 2-Prop ZInterval, Note: You can transform the percentage times the number in the sample to obtain x. In the example above we obtained x1 = by multiplying .8 x 60 = 48. We obtained the x2 = by multiplying .72 x 50 = 35.
Another note: The (1 - p) is equivalent to q.
Calculation: Using the T1-83: 2Prop ZInterval
Select STAT -> TEST -> 2 Prop ZInterval. Note select stats note data in this case You will need, calculate
This gives you a confidence interval of (-.55, .215)
Interpretation:
We are 90% confident that the true mean relating to player opinion falls between (-.55, .215)
