Question

The blood pressure of a person changes throughout the day. Suppose the systolic blood pressure of a person is measured 16 times over several days and the standard deviation of these measurements for the person is known to be σ=7.9 mmHg. Let μ be the true average blood pressure for that person and let x¯=127 be the average of the 16 measurements.

(a) Find a two-sided 94% confidence interval for μ. One can be 94% confident that the true average blood pressure μ for that person is between ___ and ___.

(b) Find a lower-bound 94% confidence interval for μ. One can be 94% confident that the true average blood pressure μ for that person is at least ____.

(c) Find an upper-bound 94% confidence interval for μ. One can be 94% confident that the true average blood pressure μ for that person is at most ____.

Answer 1

a)

94% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

127 - 1.8808 * 7.9 / sqrt(16) < < 127 + 1.8808 * 7.9 / sqrt(16)

123.285 < < 130.715

94% CI is (123.285 , 130.715)

b)

Lower bound for 94% confidence interval is

- Z * / sqrt(n)

127 - 1.5548 * 7.9 / sqrt(16)

123.929

c)

Upper bound for 94% confidence interval is

+ Z * / sqrt(n)

127 + 1.5548 * 7.9 / sqrt(16)

130.071