The blood pressure of a person changes throughout the day. Suppose the systolic

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 =7.9 mmHg. Let 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 . One can be 94% confident that the true average blood pressure for that person is between (Answer) and (Answer) .

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

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

Explanation / Answer

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=127
Standard deviation( sd )=7.9
Sample Size(n)=16
Confidence Interval = [ 127 ± Z a/2 ( 7.9/ Sqrt ( 16) ) ]
= [ 127 - 1.88 * (1.975) , 127 + 1.88 * (1.975) ]
= [ 123.287,130.713 ]

One can be 94% confident that the true average blood pressure for that person is between 123.287 and 130.713

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