If this was 2 sample independent data, what assumption(s) would we need to check? 25 normally distributed data equal variances all nip, > 5 multinomial experiment all E > 5 What is the value of our test statistic? Round to 2 decimal places. Type your answer..... 26 What is the critical value for the rejection region if this was a less than alternative hypothesis at the 1% significance level? Round to 3 decimal places. Type your answer....

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**Analysis of Distance Hit (ft) by Type of Bat**

This section presents data from JMP output comparing top-of-the-line bats to lower-priced bats to measure the distance in feet that a ball was hit.

---

**Graphs and Diagrams:**

1. **Box Plot and Dot Plot:**
   - Displays the distribution of distances for lower-priced and top-of-the-line bats.
   - The y-axis represents the "Distance in ft," ranging from 55 to 70 feet.
   - The x-axis shows "Type of Bat" with categories for "lower price" and "top of the line."
   - Each category has a dot plot overlaid on a box plot to display the variation and center.

2. **Normal Quantile Plot:**
   - Shows how the data points are distributed in relation to a normal distribution.
   - The x-axis represents the "Normal Quantile."
   - Lines for "lower price" and "top of the line" are plotted to evaluate normality.

---

**Oneway ANOVA:**

- **Summary of Fit:**
  - Rsquare: 0.250737
  - Adj Rsquare: 0.209111
  - Root Mean Square Error: 4.491628
  - Mean of Response: 60.605
  - Observations: 20

---

**Pooled t Test:**

- Comparing "top of the line" to "lower price" bats.
- **Difference:** 4.93000
- **Standard Error Difference:** 2.00872
- **t Ratio:** 2.454303
- **Degrees of Freedom (DF):** 18
- **Probability > |t|:**
  - 0.0245* (indicates statistical significance)
  - 0.0123* (indicates statistical significance)

A normal distribution curve represents the t-test results, with shaded regions corresponding to the probability values.

This analysis helps in understanding how the performance differs between the two types of bats when hitting a ball.
Transcribed Image Text:**Analysis of Distance Hit (ft) by Type of Bat** This section presents data from JMP output comparing top-of-the-line bats to lower-priced bats to measure the distance in feet that a ball was hit. --- **Graphs and Diagrams:** 1. **Box Plot and Dot Plot:** - Displays the distribution of distances for lower-priced and top-of-the-line bats. - The y-axis represents the "Distance in ft," ranging from 55 to 70 feet. - The x-axis shows "Type of Bat" with categories for "lower price" and "top of the line." - Each category has a dot plot overlaid on a box plot to display the variation and center. 2. **Normal Quantile Plot:** - Shows how the data points are distributed in relation to a normal distribution. - The x-axis represents the "Normal Quantile." - Lines for "lower price" and "top of the line" are plotted to evaluate normality. --- **Oneway ANOVA:** - **Summary of Fit:** - Rsquare: 0.250737 - Adj Rsquare: 0.209111 - Root Mean Square Error: 4.491628 - Mean of Response: 60.605 - Observations: 20 --- **Pooled t Test:** - Comparing "top of the line" to "lower price" bats. - **Difference:** 4.93000 - **Standard Error Difference:** 2.00872 - **t Ratio:** 2.454303 - **Degrees of Freedom (DF):** 18 - **Probability > |t|:** - 0.0245* (indicates statistical significance) - 0.0123* (indicates statistical significance) A normal distribution curve represents the t-test results, with shaded regions corresponding to the probability values. This analysis helps in understanding how the performance differs between the two types of bats when hitting a ball.
## Statistical Assumptions and Calculations

### Assumptions for Two-Sample Independent Data

When conducting an analysis with two independent samples, the following assumptions should be checked:

- **Normally distributed data**
- **Equal variances**
- **All \( n_i p_i > 5 \)**
- **Multinomial experiment**
- **All \( E_i > 5 \)**

### Calculation Questions

**Question 25:**  
"What is the value of our test statistic? Round to 2 decimal places."

*Type your answer:*

---

**Question 26:**  
"What is the critical value for the rejection region if this was a 'less than' alternative hypothesis at the 1% significance level? Round to 3 decimal places."

*Type your answer:*
Transcribed Image Text:## Statistical Assumptions and Calculations ### Assumptions for Two-Sample Independent Data When conducting an analysis with two independent samples, the following assumptions should be checked: - **Normally distributed data** - **Equal variances** - **All \( n_i p_i > 5 \)** - **Multinomial experiment** - **All \( E_i > 5 \)** ### Calculation Questions **Question 25:** "What is the value of our test statistic? Round to 2 decimal places." *Type your answer:* --- **Question 26:** "What is the critical value for the rejection region if this was a 'less than' alternative hypothesis at the 1% significance level? Round to 3 decimal places." *Type your answer:*
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