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ms and a standard deviation of 0.661 kilogram. Use a 0.05 significance level to test the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.4 kilograms, which is the mean for the population of all males in this particular region. Based on these results, does the vitamin supplement appear to have an effect on birth weight?

ms and a standard deviation of 0.661 kilogram. Use a 0.05 significance level to test the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.4 kilograms, which is the mean for the population of all males in this particular region. Based on these results, does the vitamin supplement appear to have an effect on birth weight?

MATLAB: An Introduction with Applications
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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### Statistical Hypothesis Testing of Birth Weights When birth weights were recorded for a simple random sample of 14 male babies born to mothers in a region taking a special vitamin supplement, the sample had a mean of 3.681 kilograms and a standard deviation of 0.661 kilograms. A 0.05 significance level is used to test the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.4 kilograms, which is the mean for the population of all males in this particular region. The task is to determine whether the vitamin supplement appears to have an effect on birth weight. Based on these results, we need to formulate the null and alternative hypotheses and choose the correct answer. #### Hypotheses Options: - **Option A:** - \( H_0: \mu = 3.4 \) - \( H_a: \mu \neq 3.4 \) - **Option B:** - \( H_0: \mu = 3.4 \) - \( H_a: \mu > 3.4 \) - **Option C:** - \( H_0: \mu \neq 3.4 \) - \( H_a: \mu = 3.4 \) - **Option D:** - \( H_0: \mu = 3.4 \) - \( H_a: \mu < 3.4 \) In this context, the correct formulation for a two-tailed test (to check if there is any difference, not specifying direction) is: - **Correct Hypotheses Formulation:** - **Null Hypothesis (\( H_0 \))**: The mean birth weight is equal to 3.4 kilograms (\( \mu = 3.4 \)). - **Alternative Hypothesis (\( H_a \))**: The mean birth weight is not equal to 3.4 kilograms (\( \mu \neq 3.4 \)). This corresponds to **Option A**. This choice aligns with checking whether the mean is different (either higher or lower) than 3.4 kilograms.
Transcribed Image Text:### Statistical Hypothesis Testing of Birth Weights When birth weights were recorded for a simple random sample of 14 male babies born to mothers in a region taking a special vitamin supplement, the sample had a mean of 3.681 kilograms and a standard deviation of 0.661 kilograms. A 0.05 significance level is used to test the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.4 kilograms, which is the mean for the population of all males in this particular region. The task is to determine whether the vitamin supplement appears to have an effect on birth weight. Based on these results, we need to formulate the null and alternative hypotheses and choose the correct answer. #### Hypotheses Options: - **Option A:** - \( H_0: \mu = 3.4 \) - \( H_a: \mu \neq 3.4 \) - **Option B:** - \( H_0: \mu = 3.4 \) - \( H_a: \mu > 3.4 \) - **Option C:** - \( H_0: \mu \neq 3.4 \) - \( H_a: \mu = 3.4 \) - **Option D:** - \( H_0: \mu = 3.4 \) - \( H_a: \mu < 3.4 \) In this context, the correct formulation for a two-tailed test (to check if there is any difference, not specifying direction) is: - **Correct Hypotheses Formulation:** - **Null Hypothesis (\( H_0 \))**: The mean birth weight is equal to 3.4 kilograms (\( \mu = 3.4 \)). - **Alternative Hypothesis (\( H_a \))**: The mean birth weight is not equal to 3.4 kilograms (\( \mu \neq 3.4 \)). This corresponds to **Option A**. This choice aligns with checking whether the mean is different (either higher or lower) than 3.4 kilograms.
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