Here are summary statistics for randomly selected weights of newborn girls: n: 152, x-28.2 hg. s-76 hg. Construct a confidence interval estimate of the mean. Use a95% confidence level. Are these results very different from the confidence interval 26.0 hg < μ < 296 hg ith only 16 sample values, x-278 hg, and s-3.4 hg?What is the confidence interval for the population mean μ?hg < μ< || hg (Round to one decimal place as needed )

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Asked May 3, 2019
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Here are summary statistics for randomly selected weights of newborn girls: n: 152, x-28.2 hg. s-76 hg. Construct a confidence interval estimate of the mean. Use a
95% confidence level. Are these results very different from the confidence interval 26.0 hg < μ < 296 hg ith only 16 sample values, x-278 hg, and s-3.4 hg?
What is the confidence interval for the population mean μ?
hg < μ< |
| hg (Round to one decimal place as needed )
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Here are summary statistics for randomly selected weights of newborn girls: n: 152, x-28.2 hg. s-76 hg. Construct a confidence interval estimate of the mean. Use a 95% confidence level. Are these results very different from the confidence interval 26.0 hg < μ < 296 hg ith only 16 sample values, x-278 hg, and s-3.4 hg? What is the confidence interval for the population mean μ? hg < μ< | | hg (Round to one decimal place as needed )

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Step 1

a.

The sample size is 152 that is reasonably large. Therefore, z-test can be used here. Let µ be the true mean weight of newborn girls.

Let x bar be the sample mean weight of newborn girls. s be the sample standard deviation. n is the sample size.

The 100(1-α)% confidence interval of µ is,

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Step 2

Here the confidence interval is 95%.

Therefore, α = 0.05. (α/2) = 0.025, 1-(α/2) = 0.975.

From the EXCEL, using the formula, “=NORM.INV(0.975,0,1)”, the critical value is 1.96.

The sample mean x bar is 28.2, s =7.6, n = 152.

Therefore the 95% confidence interval of mean weight of newborn girls is,

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Step 3

For sample size 16, t test will be used for finding the confidence interval with mean 27.8 and standard devi...

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