Question

A confidence interval for the population mean μ tells us which values of μ are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence.
You can use this idea to carry out a test of any null hypothesis H0: μ = μ0 starting with a confidence interval: reject H0ifμ0is outside the interval and fail to reject ifμ0is inside the interval.
The alternative hypothesis is always two-sided, Ha: μ ≠ μ0, because the confidence interval extends in both directions from x.
A 95% confidence interval leads to a test at the 5% significance level because the interval is wrong 5% of the time.
In general, confidence level C leads to a test at significance level α = 1 − C.

Step 1:
In Example 17.7, a medical director found mean blood pressure x = 126.07 for an SRS of 72 executives.
The standard deviation of the blood pressures of all executives is σ = 15.
Give a 90% confidence interval for the mean blood pressure μ of all executives.

a. 123.16 to 128.98
b. 122.54 to 129.46
c. 125.63 to 126.51
d. 124.30 to 127.84

Answer 1

Answer:

90% confidence interval for the mean blood pressure of all executives is 123.12 to 129.02.

The closest option is A

Step-by-step explanation:

Confidence Interval = mean + or - Error margin (E)

mean = 126.07

sd = 15

n = 72

degree of freedom = n - 1 = 72 - 1 = 71

Confidence level (C) = 90% = 0.9

Significance level = 1 - C = 1 - 0.9 = 0.1 = 10%

t-value corresponding to 71 degrees of freedom and 10% significance level is 1.6667

E = t×sd/√n = 1.6667×15/√72 = 2.95

Lower limit = mean - E = 126.07 - 2.95 = 123.12

Upper limit = mean + E = 126.07 + 2.95 = 129.02

90% confidence interval for the mean blood pressure of all executives is between a lower limit of 123.12 and an upper limit of 129.02.