If four rather than ten measurements are made, what is the expected impact on the size of the 95% confidence interval about the mean blood pressure?

If four rather than ten measurements are made, what is the expected impact on the size of the 95% confidence interval about the mean blood pressure?

• A. Increase in width
• B. Decrease in width
• C. No change
• D. Cannot be determined

Answer: (A)

A 95% confidence interval around the mean gets wider when you have fewer measurements because you have less information to pin down the true mean. The width is driven by the standard error of the mean, which shrinks as sample size grows. If the population standard deviation is known, the margin of error is proportional to sigma divided by the square root of n. Going from ten measurements to four increases the width by a factor of sqrt(10/4) ≈ 1.58, so the interval definitely broadens. If sigma is unknown, you estimate it from the data and use the t distribution. The margin of error is t with df = n−1 times s divided by sqrt(n). With fewer data points, the t multiplier is larger (for example, it’s bigger when df is 3 than when df is 9), and the sqrt(n) term in the denominator is smaller, both pushing the interval wider. In practice, fewer measurements mean more uncertainty about the mean, so the 95% confidence interval expands.

A 95% confidence interval around the mean gets wider when you have fewer measurements because you have less information to pin down the true mean. The width is driven by the standard error of the mean, which shrinks as sample size grows.

If the population standard deviation is known, the margin of error is proportional to sigma divided by the square root of n. Going from ten measurements to four increases the width by a factor of sqrt(10/4) ≈ 1.58, so the interval definitely broadens.

If sigma is unknown, you estimate it from the data and use the t distribution. The margin of error is t with df = n−1 times s divided by sqrt(n). With fewer data points, the t multiplier is larger (for example, it’s bigger when df is 3 than when df is 9), and the sqrt(n) term in the denominator is smaller, both pushing the interval wider. In practice, fewer measurements mean more uncertainty about the mean, so the 95% confidence interval expands.