When 14 different second-year medical students at Bellevue...

When 14 different second-year medical students at Bellevue Hospital measured the blood pressure of the same person, they obtained the results listed below. Assuming that the population standard deviation is known to be $10 \mathrm{mmHg}$, construct a $95 \%$ confidence interval estimate of the population mean. Ideally, what should the confidence interval be in this situation? $$\begin{array}{rrrrrrrrrrrrrr} 138 & 130 & 135 & 140 & 120 & 125 & 120 & 130 & 130 & 144 & 143 & 140 & 130 & 150 \end{array}$$

When 14 different second-year medical students at Bellevue Hospital measured the blood pressure of the same person, they obtained the results listed below. Assuming that the population standard deviation is known to be $10 \mathrm{mmHg}$, construct a $95 \%$ confidence interval estimate of the population mean. Ideally, what should the confidence interval be in this situation?
$$\begin{array}{rrrrrrrrrrrrrr}
138 & 130 & 135 & 140 & 120 & 125 & 120 & 130 & 130 & 144 & 143 & 140 & 130 & 150
\end{array}$$

Key Concepts

Margin of Error

The margin of error represents the extent of the uncertainty around the sample estimate and is calculated by multiplying the critical value by the standard error of the mean. It defines the width of the confidence interval on either side of the sample mean, indicating how much the sample mean could vary from the population mean.

Central Limit Theorem

The Central Limit Theorem states that, regardless of the original population distribution, the distribution of the sample means will tend to be normal if the sample size is sufficiently large. This principle justifies the use of the normal distribution in constructing confidence intervals for the population mean.

Confidence Interval

A confidence interval is a range of values derived from sample statistics that is likely to contain the true value of an unknown population parameter. It provides an estimate along with a measure of uncertainty, helping to assess the reliability of the sample estimate.

Known Population Standard Deviation and Z-Distribution

When the population standard deviation is known, the normal (Z) distribution is used to construct the confidence interval for a population mean. This approach allows the use of critical values from the standard normal distribution to compute the interval, assuming that the sampling distribution of the mean is normal or approximately normal.

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