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 = cms = cm

(b) Compute a 90% 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     cmupper limit     cm

Answer:

(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 = 15.8 cm

s = 3.5 cm

(b)

Compute a 90% confidence interval for the population mean μ of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site.

lower limit  13.8 cm

upper limit  17.8 cm

Step-by-step explanation

Data

15.9 13.4 22.1 12.7 13.1 19.6 11.7 13.5 17.7 18.1

sample size, n = 10

(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 = 15.78 = 15.8 cm

s = 3.460828 = 3.5 cm

(b)

Compute a 90% confidence interval for the population mean μ of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site.

Since population standard deviation is unknown, construct a t confidence interval

?=x?±t∗(?s/underootn?)?

t critical value for 90% confidence interval

degrees of freedom, df=n-1 =10-1 =9

?α? =1-0.9 =0.10

t value with df=9 and upper-tail area=0.1/2=0.05

t = 1.8331

90% confidence interval

?=15.78±1.8331(?3.4608?/underoot10)?

?=15.78±2.006147?

Lower limit = 15.78 - 2.006147 = 13.773853 = 13.8

Upper limit = 15.78 + 2.006147 = 17.786147 = 17.8

lower limit  13.8 cm

upper limit  17.8 cm