Fifty people in the civilian labor force are randomly selected and the sample average age iscomputed to be 36.4.(a) find a 90% confidence interval for the mean age, ? , of all people in the civilian laborforce. assume that the population standard deviation for the ages of civilian labor force is12.1 years. interpret the confidence interval.(b) it is being claimed that the mean age of the population of civilian labor force is 40. whatdo you conclude based on the confidence interval?

a) The 90% confidence interval would be given by (33.594;39.206)  

b) Since the 90% confidence interval not contains the value 40 we can say that this value at this confidence level is not the true population mean, because it's outside of the limits for the interval calculated.

Step-by-step explanation:

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".  

Part a

represent the sample mean  

population mean (variable of interest)  

represent the population standard deviation  

n=50 represent the sample size  

90% confidence interval  

The confidence interval for the mean is given by the following formula:  

(1)  

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

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

So on this case the 90% confidence interval would be given by (33.594;39.206)  

Part b

Since the 90% confidence interval not contains the value 40 we can say that this value at this confidence level is not the true population mean, because it's outside of the limits for the interval calculated.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: