https://file.aiquickdraw.com/mathbot/file/17267396999392cvh762h.jpg

To solve this problem, we need to conduct a hypothesis test to determine whether the external temperature conditions (locations A and B) have a statistically significant effect on the height growth of children at a 5% significance level.

### Steps:
1. **Define Hypotheses:**
   - **Null Hypothesis (H₀):** There is no significant difference in height growth between the two locations (temperature conditions), i.e., the mean heights from location A and location B are the same.
   - **Alternative Hypothesis (H₁):** There is a significant difference in height growth between the two locations, i.e., the mean heights from location A and location B are different.

2. **Data:**
   - Heights for **Location A**: 98, 102, 96, 104, 100
   - Heights for **Location B**: 100, 105, 98, 102, 104

3. **Type of Test:**
   Since we are comparing two independent samples (location A and location B), we can use a **two-sample t-test** for the means.

4. **Level of Significance:**
   We are given a significance level of 5% (α = 0.05).

Let me now compute the necessary statistics (mean, standard deviation, t-statistic) and perform the t-test.### Results of the Two-Sample t-Test:
- **Mean for Location A**: 100.0
- **Mean for Location B**: 101.8
- **Standard deviation for Location A**: 3.16
- **Standard deviation for Location B**: 2.86
- **t-statistic**: -0.943
- **p-value**: 0.373

### Conclusion:
The p-value is 0.373, which is much larger than the significance level of 0.05. Therefore, we **fail to reject the null hypothesis**.

### Interpretation:
There is no statistically significant evidence at the 5% level to suggest that temperature conditions between locations A and B affect the height growth of children.

---

Would you like more details on the t-test procedure or have any questions? 

Here are some related questions you might find helpful:
1. How is the t-statistic calculated in a two-sample t-test?
2. What assumptions must be satisfied to use a two-sample t-test?
3. How can you interpret the p-value in hypothesis testing?
4. What is the difference between paired and unpaired t-tests?
5. How can you adjust for unequal variances in a t-test?

**Tip:** Always check whether the variances of the two groups are equal before conducting a t-test; if not, consider using Welch's t-test.

A study conducted stating does the temperature conditions affect the growth of height in children. The data was collected from two different locations A and location B. Check whether the external condition of temperature is affecting the growth or not at a level of significance of 5%. Data: A: [98, 102, 96, 104, 100], B: [100, 105, 98, 102, 104].

Conduct a two-sample t-test to evaluate whether external temperature conditions at two different locations A and B significantly affect children's height growth at a 5% significance level. Learn how to calculate the t-statistic, p-value, and interpret the results.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation