Questions: When birth weights were recorded for a simple random sample of 12 male babies born to mothers in a region taking a special vitamin supplement, the sample had a mean of 3.658 kilograms 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 3.38 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? P-value = 0.173 (Round to three decimal places as needed.) State the conclusion. A. Do not reject H0. There is sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do appear to have an effect on birth weight. B. Reject H0. There is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do not appear to have an effect on birth weight. C. Do not reject H0. There is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do not appear to have an effect on birth weight. D. Reject H0. There is sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do appear to have an effect on birth weight.

When birth weights were recorded for a simple random sample of 12 male babies born to mothers in a region taking a special vitamin supplement, the sample had a mean of 3.658 kilograms 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 3.38 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? P-value = 0.173 (Round to three decimal places as needed.) State the conclusion. A. Do not reject H0. There is sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do appear to have an effect on birth weight. B. Reject H0. There is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do not appear to have an effect on birth weight. C. Do not reject H0. There is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do not appear to have an effect on birth weight. D. Reject H0. There is sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do appear to have an effect on birth weight.
Transcript text: When birth weights were recorded for a simple random sample of 12 male babies born to mothers in a region taking a special vitamin supplement, the sample had a mean of 3.658 kilograms 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 3.38 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? P-value $=0.173$ (Round to three decimal places as needed.) State the conclusion. A. Do not reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do appear to have an effect on birth weight. B. Reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do not appear to have an effect on birth weight. C. Do not reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do not appear to have an effect on birth weight. D. Reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.38 kilograms. Vitamin supplements do appear to have an effect on birth weight.
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Solution

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Solution Steps

Step 1: Given Data

We have a sample of 12 male babies with the following statistics:

  • Sample Mean (\(\bar{x}\)): \(3.658\) kg
  • Sample Standard Deviation (\(s\)): \(0.661\) kg
  • Hypothesized Population Mean (\(\mu_0\)): \(3.38\) kg
  • Sample Size (\(n\)): \(12\)
  • Significance Level (\(\alpha\)): \(0.05\)
Step 2: Calculate Standard Error

The Standard Error (\(SE\)) is calculated using the formula: \[ SE = \frac{s}{\sqrt{n}} = \frac{0.661}{\sqrt{12}} \approx 0.1908 \]

Step 3: Calculate Test Statistic

The test statistic (\(t\)) is calculated using the formula: \[ t = \frac{\bar{x} - \mu_0}{SE} = \frac{3.658 - 3.38}{0.1908} \approx 1.4569 \]

Step 4: Calculate P-value

For a two-tailed test, the P-value is calculated as: \[ P = 2 \times (1 - T(|z|)) \approx 0.1731 \]

Step 5: Conclusion

Since the P-value \(0.1731\) is greater than the significance level \(\alpha = 0.05\), we do not reject the null hypothesis (\(H_0\)). This indicates that there is not sufficient evidence to support the claim that the mean birth weight for all male babies of mothers given vitamins is different from \(3.38\) kg. Therefore, vitamin supplements do not appear to have an effect on birth weight.

Final Answer

The answer is C. \\(\boxed{C}\\)

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