Respuesta :
Answer:
[tex]128.07-1.64\frac{15}{\sqrt{72}}=125.16[/tex]
[tex]128.07+ 1.64\frac{15}{\sqrt{72}}=130.98[/tex]
b. 125.16 to 130.98
Step-by-step 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".
[tex]\bar X =128.07[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=15[/tex] 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:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], 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 [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]128.07-1.64\frac{15}{\sqrt{72}}=125.16[/tex]
[tex]128.07+ 1.64\frac{15}{\sqrt{72}}=130.98[/tex]
b. 125.16 to 130.98
