Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a0.01significance level. ### Hypothesis Testing Using IQ Scores**Data Overview:**The provided table lists IQ scores for samples of subjects with medium and high lead levels in their blood. The data compares IQ scores between these two groups to determine if lead levels affect intelligence differently.**Objective:**Test the claim that the mean IQ score for subjects with medium lead levels is higher than for those with high lead levels, using a 0.01 significance level. Assume the samples are independent, and do not assume equal population standard deviations.**IQ Scores Data:**- **Medium Lead Level:** - Scores: 72, 81, 92, 85, 80, 97, 83, 92, 100, 111, 91- **High Lead Level:** - Number of subjects (n₂) = 11 - Mean (x̄₂) = 87.308 - Standard Deviation (s₂) = 10.578**Hypotheses:**- **Null Hypothesis (H₀):** - Option B: μ₁ ≤ μ₂- **Alternative Hypothesis (H₁):** - μ₁ > μ₂**Calculation Requirements:**- **Test Statistic:** [____] (Round to two decimal places as needed.)- **P-value:** [____] (Round to three decimal places as needed.)**Conclusion:**Choose from the following conclusions based on the test statistic and P-value:- **A.** Reject the null hypothesis. There is sufficient evidence to support the claim that subjects with medium lead levels have higher IQ scores.- **B.** Reject the null hypothesis. There is not sufficient evidence to support the claim.- **C.** Fail to reject the null hypothesis. There is sufficient evidence to support the claim.- **D.** Fail to reject the null hypothesis. There is not sufficient evidence to support the claim.**Instructions:**Complete the analysis by determining the test statistic and P-value, then select the appropriate conclusion based on the results.

Calculating sample mean and sample standard deviation for medium lead level:…

Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.01 significance level. E Click the icon to view the data table of IQ scores. Test the claim that the mean IQ scores for subjects with medium lead levels is higher than the mean for subjects with high lead levels. What are the null and alternative hypotheses? Assume that population 1 consists of subjects with medium lead levels and population 2 consists of subjects with high lead levels. O A. Ho: H1 H2 H: H1> H2 O B. Ho: H1 SH2 H: H1>H2 OC. Ho: H1 = H2 O D. Ho: H1 = H2 IQ Scores The test statistic is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) Medium Lead Level O High Lead Level State the conclusion for the test. 72 n2 = 11 81 92 O A. Reject the null hypothesis. There is sufficient evidence to support the claim that subjects with mediur X2 = 87.308 O B. Reject the null hypothesis. There is not sufficient evidence to support the claim that subjects with me $2 = 10.578 OC. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that subjects with r 83 O D. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that subjects w 92 100

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of IQ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a

0.01

significance level.

### Hypothesis Testing Using IQ Scores

**Data Overview:**

The provided table lists IQ scores for samples of subjects with medium and high lead levels in their blood. The data compares IQ scores between these two groups to determine if lead levels affect intelligence differently.

**Objective:**

Test the claim that the mean IQ score for subjects with medium lead levels is higher than for those with high lead levels, using a 0.01 significance level. Assume the samples are independent, and do not assume equal population standard deviations.

**IQ Scores Data:**

- **Medium Lead Level:**
- Scores: 72, 81, 92, 85, 80, 97, 83, 92, 100, 111, 91

- **High Lead Level:**
- Number of subjects (n₂) = 11
- Mean (x̄₂) = 87.308
- Standard Deviation (s₂) = 10.578

**Hypotheses:**

- **Null Hypothesis (H₀):**
- Option B: μ₁ ≤ μ₂
- **Alternative Hypothesis (H₁):**
- μ₁ > μ₂

**Calculation Requirements:**

- **Test Statistic:** [____] (Round to two decimal places as needed.)
- **P-value:** [____] (Round to three decimal places as needed.)

**Conclusion:**

Choose from the following conclusions based on the test statistic and P-value:

- **A.** Reject the null hypothesis. There is sufficient evidence to support the claim that subjects with medium lead levels have higher IQ scores.
- **B.** Reject the null hypothesis. There is not sufficient evidence to support the claim.
- **C.** Fail to reject the null hypothesis. There is sufficient evidence to support the claim.
- **D.** Fail to reject the null hypothesis. There is not sufficient evidence to support the claim.

**Instructions:**

Complete the analysis by determining the test statistic and P-value, then select the appropriate conclusion based on the results.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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