Ho: There is no association between how the ball is rebounded and the number of shots made (u = 0). Ha: There is an association between how the ball is rebounded and the number of shots made (u, # 0). The students found the following results for the number of baskets made. Rebounded Self-rebounded Difference Mean 3.875 3.000 0.875 Standard deviation 2.399 2.320 1.977 Assuming a true null hypothesis, we simulated this study and found 5,000 mean differences that are shown in the null distribution below. Mean 0.000 SD 0.336 -1.20 -0.90 -0.60 -0.30 0.00 0.30 0.60 0.90 1.20 Average difference (a) Use the 2SD method to create an approximate 95% confidence interval for the mean difference in number of shots made (rebounded-self-rebounded) for the population of interest. Round answer to 3 decimal places, e.g. 0.298.
Ho: There is no association between how the ball is rebounded and the number of shots made (u = 0). Ha: There is an association between how the ball is rebounded and the number of shots made (u, # 0). The students found the following results for the number of baskets made. Rebounded Self-rebounded Difference Mean 3.875 3.000 0.875 Standard deviation 2.399 2.320 1.977 Assuming a true null hypothesis, we simulated this study and found 5,000 mean differences that are shown in the null distribution below. Mean 0.000 SD 0.336 -1.20 -0.90 -0.60 -0.30 0.00 0.30 0.60 0.90 1.20 Average difference (a) Use the 2SD method to create an approximate 95% confidence interval for the mean difference in number of shots made (rebounded-self-rebounded) for the population of interest. Round answer to 3 decimal places, e.g. 0.298.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Is a basketball player's ability to make free throws different when they get their own rebound or when someone else gets their rebound for them? This is what student researchers wanted to explore. The researchers used students (20 females and 20 males) taking a college physical education class as their subjects. The students each attempted 10 shots from the free throw line where they had to get their own rebound and 10 shots where someone else got their rebound and passed the ball back to them while they stayed on the free throw line. They randomly determined the order that they took these shots, with some getting their own rebounds first and some having someone else get the rebounds first. Here are the hypotheses in the picture:
Transcribed Image Text:**Title:** Exploring the Relationship Between Rebounding Method and Number of Shots Made
**Introduction:**
In a study examining the association between rebounding methods and basketball shot success rates, two hypotheses were tested:
- \(H_0\): There is no association between how the ball is rebounded and the number of shots made (\(\mu_d = 0\)).
- \(H_a\): There is an association between how the ball is rebounded and the number of shots made (\(\mu_d \neq 0\)).
**Study Results:**
A comparison of the mean number of baskets made in two scenarios was conducted:
| | Rebounded | Self-rebounded | Difference |
|-----------------|-----------|----------------|------------|
| **Mean** | 3.875 | 3.000 | 0.875 |
| **Standard Deviation** | 2.399 | 2.320 | 1.977 |
**Simulation Study:**
Assuming the null hypothesis is true, 5,000 simulations were conducted to generate a distribution of mean differences. The results are displayed in a histogram:
- **Histogram Details:**
- The x-axis represents the average difference in the number of shots made.
- The y-axis shows the frequency of these differences.
- The distribution is centered around a mean of 0.000 with a standard deviation of 0.336, illustrating a normal distribution.
**Analysis:**
(a) **Confidence Interval Calculation:**
Use the 2SD method to construct a 95% confidence interval for the mean difference in the number of shots made (rebounded - self-rebounded). Round your answer to three decimal places.
- **Confidence Interval:** (_____, _____)
(b) **Evidence Evaluation:**
Based on your confidence interval from part (a), assess whether there is strong evidence that the mean number of shots made differs between self-rebounding and when someone else rebounds. Explain your reasoning:
- **Options:**
- Yes, because the entire interval is positive, indicating strong evidence against the null hypothesis.
- Yes, because the interval does not include zero, showing evidence against the null hypothesis.
- No, because the interval includes both positive and negative numbers, indicating no strong evidence against the null hypothesis.
This educational exercise provides a practical insight into statistical hypothesis testing and confidence interval interpretation, an essential skill in data analysis.
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