The diastolic blood pressure readings for 15 patients were...

The diastolic blood pressure readings for 15 patients were determined using two techniques: the standard method used by medical personnel and a method using an electronic device with a digital readout. The results were as follows: Assuming blood pressure is normally distributed, determine the $90 \%$ confidence interval for the mean difference in the two readings, where $d=$ standard method - digital readout.

Key Concepts

Degrees of Freedom

Degrees of freedom, in the context of a paired t-test, usually equal the number of pairs minus one. This value is important because it influences the shape of the t-distribution and determines the critical value needed to construct the confidence interval.

Standard Error

The standard error of the mean difference measures the variability of the sample mean difference. It is calculated using the sample standard deviation of the differences divided by the square root of the number of pairs, and it plays a key role in determining the width of the confidence interval.

t-Distribution

The t-distribution is used instead of the normal distribution when dealing with small sample sizes and an unknown population variance. It accounts for additional uncertainty due to estimating the standard deviation from the sample data, especially crucial in paired comparisons.

Confidence Interval

A confidence interval is a range of values, derived from the sample data, that is believed to contain the true population parameter with a specified level of confidence. In this context, it provides an estimated range for the mean difference between the two measurement methods.

Paired Samples

In statistics, paired samples refer to data collected in pairs where each subject or experimental unit is measured twice under different conditions. This design reduces variability since comparisons are made within the same subject, leading to more precise estimates of the effect of the treatment or condition.

Difference Variable

The difference variable is created by subtracting one measurement from the other for each pair. This variable captures the change between the two measurements and is analyzed to estimate the mean difference, providing insight into any systematic bias between the two methods.

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