Sherds of clay vessels were put together to reconstruct rim

Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels at the Wind Mountain archaeologicaI 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.) (b) Compute a 95% confidence interval for the population mean mu of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site. (Round your answers to one decimal place.)

Solution

mean= 15.78 =15.8 (rounding to 1 dec. place)
s.d= 3.28323 =3.3 (rounding)

(b) 95% conf. interval for population mean:
lower limit = mean - (z * s.d / sqrt(n) ) =15.78 - (1.959964 * 3.28323 /sqrt(10) = 15.78-2.035 =13.7
upper limit= mean + (z * s.d / sqrt(n) ) = 15.78+ 2.035 =17.8

2) success= the workers who responded in a positive way that they are satisfied from doing the job

prob. of success=p = 1599/ 2993 = 0.534

population standard error = sqrt ( p(1-p) / n) = 0.534(1- 0.534) / sqrt( 2993) =0.0091

z-score for 90% conf =1.644854
lower limit = 0.534 - ( 1.644854 * 0.0091 ) = 0.519
upper limit= 0.534 +  ( 1.644854 * 0.0091 ) = 0.549