Question

The blood pressure of a person changes throughout the day. Suppose the systolic blood pressure of a person is measured 24 times over several days and the standard deviation of these measurements for the person is known to be σ=9 σ = 9 mmHg. Let μ μ be the true average blood pressure for that person and let x¯=96 x ¯ = 96 be the average of the 24 measurements. (a) Find a two-sided 91% confidence interval for μ.μ. One can be 91% confident that the true average blood pressure μμ for that person is between _ and _

(b) Find a lower-bound 91% confidence interval for μ.μ. One can be 91% confident that the true average blood pressure μμ for that person is at least _

(c) Find an upper-bound 91% confidence interval for μ.μ. One can be 91% confident that the true average blood pressure μμ for that person is at most _

Answer 1

(a)

n = 24     

x-bar = 96     

s = 9     

% = 91     

Standard Error, SE = σ/√n =    9 /√24 = 1.8371

z- score = 1.6954

The 91% confidence interval is [96 - 1.6954 * 1.8371, 96 + 1.6954 * 1.8371] = [92.885, 99.115]

One can be 91% confident that the true average blood pressure μ for that person is between 92.885 and 99.115

(b)

z- score = -1.3408

The lower bound for 91% confidence interval is 96 - 1.3408 * 1.8371 = 93.537

One can be 91% confident that the true average blood pressure μμ for that person is at least 93.537

(c)

z- score = 1.3408

The upper bound for 91% confidence interval is 96 + 1.3408 * 1.8371] = 98.463

One can be 91% confident that the true average blood pressure μμ for that person is at most 98.463

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