Question

Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels 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) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

x =	cm
s =	cm

(b) Compute a 98% confidence interval for the population mean μ of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site. (Round your answers to one decimal place.)

lower limit	cm
upper limit	cm

Answer 1

The sample size is n = 10. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	15.9	252.81
	13.4	179.56
	22.1	488.41
	12.7	161.29
	13.1	171.61
	19.6	384.16
	11.7	136.89
	13.5	182.25
	17.7	313.29
	18.1	327.61
Sum =	157.8	2597.88

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

The provided sample mean is 15.78 and the sample standard deviation is s = 3.461 . The size of the sample is n = 10 and the required confidence level is 98%.

The number of degrees of freedom are df = 10 - 1 = 9 , and the significance level i α=0.02.

Based on the provided information, the critical t-value for α=0.02 and df = 9 degrees of freedom is t_c = 2.821.

The 98% confidence for the population mean is computed using the following expression

  

Therefore, based on the information provided, the 98 % confidence for the population mean is

CI = (12.692, 18.868)

which completes the calculation.