Shards of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels found at the Wind Mountain archaeological site. A random sample of ceramic vessels gave the following rim diameters (in centimeters):

15.9 - 13.4 - 22.1 - 12.7 - 13.1 - 19.6 - 11.7 - 13.5 - 17.7 - 18.1

(A) With mean and sample deviation verify that x bar is about equal to 15.8 cm and s equal to 3.5 cm.

(B) Compute an 80% confidence interval for the population mean (mhu) of rim diameters for such ceramic vesselsfound at the Wind Mountain archaelogical site.

a) In order to calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

The sample deviation calculated

b)    

So on this case the 80% confidence interval would be given by (14.27;17.33)  

Step-by-step explanation:

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".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Part a

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

  (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

The sample deviation calculated

Part b

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.80 or 80%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.1,9)".And we see that

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

So on this case the 80% confidence interval would be given by (14.27;17.33)    

x/3-10=8

x/3=18

x=48