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 32 times over several days and the standard deviation of these measurements for the person is known to be ?=9.3 mmHg. Let ? be the true average blood pressure for that person and let x¯=137 be the average of the 32 measurements. (a) Find a two-sided 98% confidence interval for ?. One can be 98% confident that the true average blood pressure ? for that person is between _____ and ______ . (b) Find a lower-bound 98% confidence interval for ?. One can be 98% confident that the true average blood pressure ? for that person is at least _____ . (c) Find an upper-bound 98% confidence interval for ?. One can be 98% confident that the true average blood pressure ? for that person is at most _____

Is there a way to do this without the Z table? we are not allowed to use it for tests and i do not know how to do it any other way.  

Explanation / Answer

Mean(x) = 137

Std Dev(s) = 9.3

n = 32

Standard Error (se) = s/n1/2 = 1.64

At 98%,

Zcritical = 2.33

98% CI = x +/- Zcritical * se = 137 +/- 2.33*1.64 = (133.17,140.83)

a)

One can be 98% confident that the true average blood pressure for that person is between 133.17 and 140.83

b) One can be 98% confident that the true average blood pressure for that person is at least 133.17.

c) One can be 98% confident that the true average blood pressure for that person is at most 140.83

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