Question

Select the 90% confidence interval for the mean blood pressure ???? of all executives in this age group, assuming the standard deviation is the same for all males 50‐59 years of age.

a. 125.80 to 130.34
b. 125.16 to 130.98
c. 124.61 to 131.53
d. 123.52 to 132.62

Answer 1

`128.07-1.64(15)/(√(72))=125.16`

`128.07+ 1.64(15)/(√(72))=130.98`

b. 125.16 to 130.98

Explanation:

Assuming the following info: " A medical director found mean blood pressure ¯=128.07 for an SRS of 72 male executives between the ages of 50 and 59. The standard deviation of the blood pressures of all males 50–59 years of age is σ=15. Select the 90% confidence interval for the mean blood pressure of all executives in this age group, assuming the standard deviation is the same for all males 50‐59 years of age."

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

`\bar X =128.07` represent the sample mean for the sample

`\mu` population mean (variable of interest)

`\sigma=15` represent the population standard deviation

n=72 represent the sample size

Calculate the confidence interval

Since the sample size is large enough n>30. The confidence interval for the mean is given by the following formula:

`\bar X \pm z_(\alpha/2)(\sigma)/(√(n))` (1)

Since the Confidence is 0.90 or 90%, the value of
`\alpha=0.1` and
`\alpha/2 =0.05`, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that
`z_(\alpha/2)=1.64`

Now we have everything in order to replace into formula (1):

`128.07-1.64(15)/(√(72))=125.16`

`128.07+ 1.64(15)/(√(72))=130.98`

b. 125.16 to 130.98