Question

In: Statistics and Probability

Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels...


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

Solutions

Expert Solution

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.


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