Correction: See Table Below, Thank You! Comparing two population means (independ
ID: 3233238 • Letter: C
Question
Correction: See Table Below, Thank You!
Comparing two population means (independent samples, sigmas unknown) Most consumers are not diamond experts, so many rely on an independent certification body to determine a diamond's value. Diamonds are assessed on four characteristics, referred to as the "four Cs": carat weight, color, clarity, and cut. Several certification bodies issue diamond grading reports, including the Gemological Institute of America (GIA), the Hoge Raad voor Diamant (HRD), and the International Gemological Institute (IGI). If a certification body Is recognized as strict In Its grading, diamonds certified by that body may sell for higher prices than diamonds with the same grades that are certified by a different body. Compare the prices of diamonds graded by one certifier to the prices of diamonds graded by a different certifier to learn whether one population carries a price premium. The Diamonds data set in the following DataView tool contains data on the carat weight, color, clarity, certification body, and selling price of a random sample of 308 round-cut diamond stones. [Source: Singfat Chu, Journal of Statistics Education Data Archive.] Define population 1 as diamonds certified by GIA and population 2 as diamonds certified by IGI. Similarly, define mu_1 as the mean price of diamonds certified by GIA and mu_2 as the mean price of diamonds certified by IGI. The point estimate of mu_2 - mu_2 is _____. The population standard deviations sigma_1 and sigma_2 are unknown. Use the Distributions tool and the DataView tool to develop a 90% confidence interval for the difference between the mean prices of diamonds certified by the two certifiers. The 90% confidence interval for the difference between the two population means is _____ to _____. data set in the following DataView tool contains data on the carat weight, color, clarity, certification body, and selling price of random sample of 308 round-cut diamond stones. [Source: Singfat Chu, Journal of Statistics Education Data Archive.]Explanation / Answer
Note: since there are some missing observations and the cumbersome process of typing out 308 observations, i will explain the process to solve the problem.
point estimate, µ1 - µ2, µ1 = mean of price only for the 149 or so observations shown above where the certification body is GIA. µ2= mean of price only for the 152 to 229 or so observations shown above where the certification body is IGI
90% Confidence Interval
Find s1 and s2, standard deviations for the price of GIA certified diamonds and IGI certified diamonds. Use excel or r or any other statistical software.
standard error, SEx1-x2 = sqrt [ s21 / n1 + s22 / n2 ]
Degree of freedom, DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }, round it off to the nearest whole number
Find the critical t value for degree of freedom = DF and significance value 0.1
margin of error (ME): ME = critical value * standard error
CI = sample statistic + margin of error, sample statistic is µ1 - µ2