A professional basketball player has embarked on a program to study his ability to shoot foul shots. On each day in which a game is not scheduled, he intends to shoot 100 foul shots. He maintains records over a period of 40 days of practice, with the results below.
Foul Shots Made Number Taken
73 100
75 100
69 100
72 100
77 100
71 100
68 100
70 100
67 100
74 100
75 100
72 100
70 100
74 100
73 100
76 100
69 100
68 100
72 100
70 100
64 100
67 100
72 100
70 100
74 100
76 100
75 100
78 100
76 100
80 100
78 100
83 100
84 100
81 100
86 100
85 100
86 100
87 100
85 100
85 100
Construct a p chart for the proportion of successful foul shoots.
Do you think that the player's should shooting process is in statistical control? Why or why not?
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To construct a p-chart for the proportion of successful foul shots, we need to calculate the proportion of successful shots for each day of practice.
First, let's calculate the proportion of successful shots for each day:
- For Day 1: 73/100 = 0.73
- For Day 2: 75/100 = 0.75
- For Day 3: 69/100 = 0.69
...
- For Day 40: 85/100 = 0.85
Now we have the proportions for each day. The p-chart will plot these proportions over time to see if there are any patterns or variations. Given that we have 40 days of practice, we can easily create the p-chart using a spreadsheet software or statistical software like Excel or Minitab.
Here's a step-by-step process to create a p-chart using Excel:
1. Open Excel and create two columns: one for the Day numbers and another for the proportions of successful shots.
2. Enter the Day numbers from 1 to 40 in the first column.
3. In the second column, enter the proportion of successful shots for each day.
4. Calculate the overall mean proportion (p-bar) by adding up all the proportions and dividing by the number of days (40). This will give you the average proportion.
5. Calculate the upper control limit (UCL) and lower control limit (LCL) for the p-chart. The UCL represents the upper boundary of acceptable variation, and the LCL represents the lower boundary.
UCL = p-bar + 3 * √(p-bar(1 - p-bar)/n)
LCL = p-bar - 3 * √(p-bar(1 - p-bar)/n)
where p-bar is the mean proportion and n is the number of days.
6. Create a line graph using the Day numbers as the x-axis and the proportions of successful shots as the y-axis.
7. Add a horizontal line for the UCL and LCL on the graph.
If the proportion of successful shots falls within the UCL and LCL boundaries, the shooting process is considered in statistical control, indicating that the player's performance is consistent and predictable. However, if the proportion of successful shots goes beyond these boundaries or shows any extreme patterns or trends, this suggests that the shooting process might be out of control and subject to non-random variation.
By following these steps and analyzing the p-chart, you will be able to determine if the player's shooting process is in statistical control based on the recorded data.