populations having normal distributions. Use a 0.05 significance level to test the claim that the va kull breadths in 4000 B.C. is the same as the variation in A.D. 150. 4000 B.C. A.D. 150 n 30 30 AH₂0₁ #0₂ H₁ 2 What are the null and alternative hypotheses? 2 ²H₂O² = 0₂ Ho 2 2 H₁ <0₂ 131.92 mm 136.92 mm dentify the test statistic. 5.16 mm 5.31 mm (Round to two decimal places as needed.) BH₂0²= 6₂ H₁0² #0 H₁₂ D. Hoo ₁ = 0 ₂ H₁0²203 н,
populations having normal distributions. Use a 0.05 significance level to test the claim that the va kull breadths in 4000 B.C. is the same as the variation in A.D. 150. 4000 B.C. A.D. 150 n 30 30 AH₂0₁ #0₂ H₁ 2 What are the null and alternative hypotheses? 2 ²H₂O² = 0₂ Ho 2 2 H₁ <0₂ 131.92 mm 136.92 mm dentify the test statistic. 5.16 mm 5.31 mm (Round to two decimal places as needed.) BH₂0²= 6₂ H₁0² #0 H₁₂ D. Hoo ₁ = 0 ₂ H₁0²203 н,
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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![### Analysis of Skull Measurements Over Time
Researchers have measured skulls from two different time periods to investigate potential cultural interbreeding by comparing maximal skull breadth variations. The data below is used to test this claim at a significance level of 0.05. The comparison involves:
#### Dataset Summary:
- **Time Periods:**
- **4000 B.C.**
- Sample size (\(n\)) = 30
- Mean (\(\bar{x}\)) = 131.92 mm
- Standard deviation (\(s\)) = 5.16 mm
- **A.D. 150**
- Sample size (\(n\)) = 30
- Mean (\(\bar{x}\)) = 136.92 mm
- Standard deviation (\(s\)) = 5.31 mm
The hypothesis to be tested is whether the variation in skull breadths is the same between these two time periods.
#### Hypothesis Testing:
- **Null Hypothesis (H₀):** \(\sigma_1^2 = \sigma_2^2\) (The populations have equal variances.)
- **Alternative Hypothesis (H₁):** \(\sigma_1^2 \neq \sigma_2^2\) (The populations do not have equal variances.)
**Correct Choice of Hypotheses:**
- Option **B** is the correct choice, representing the hypotheses as \( H_0: \sigma_1^2 = \sigma_2^2 \) and \( H_1: \sigma_1^2 \neq \sigma_2^2 \).
#### Calculation:
- **Determine the Test Statistic:**
- Calculate the test statistic \( F \) using the formula:
\[
F = \frac{s_1^2}{s_2^2}
\]
- Round the F statistic to two decimal places as needed.
This test helps determine if the variation in skull breadths between the two time periods is statistically significant, indicating whether cultural interbreeding could have occurred.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a61b2c2-d497-421c-be53-2739493073dd%2Ffe65d8c4-f0b0-487b-bfc2-09d8c1fa9c77%2Fwsgqeo7_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Skull Measurements Over Time
Researchers have measured skulls from two different time periods to investigate potential cultural interbreeding by comparing maximal skull breadth variations. The data below is used to test this claim at a significance level of 0.05. The comparison involves:
#### Dataset Summary:
- **Time Periods:**
- **4000 B.C.**
- Sample size (\(n\)) = 30
- Mean (\(\bar{x}\)) = 131.92 mm
- Standard deviation (\(s\)) = 5.16 mm
- **A.D. 150**
- Sample size (\(n\)) = 30
- Mean (\(\bar{x}\)) = 136.92 mm
- Standard deviation (\(s\)) = 5.31 mm
The hypothesis to be tested is whether the variation in skull breadths is the same between these two time periods.
#### Hypothesis Testing:
- **Null Hypothesis (H₀):** \(\sigma_1^2 = \sigma_2^2\) (The populations have equal variances.)
- **Alternative Hypothesis (H₁):** \(\sigma_1^2 \neq \sigma_2^2\) (The populations do not have equal variances.)
**Correct Choice of Hypotheses:**
- Option **B** is the correct choice, representing the hypotheses as \( H_0: \sigma_1^2 = \sigma_2^2 \) and \( H_1: \sigma_1^2 \neq \sigma_2^2 \).
#### Calculation:
- **Determine the Test Statistic:**
- Calculate the test statistic \( F \) using the formula:
\[
F = \frac{s_1^2}{s_2^2}
\]
- Round the F statistic to two decimal places as needed.
This test helps determine if the variation in skull breadths between the two time periods is statistically significant, indicating whether cultural interbreeding could have occurred.
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