Attempts: Keep the Highest: 16 4. Inference about the difference between two means (unequal variances) Most consumers are not diamond experts, so many rely on an Independent certification body to determine a diamond's value. Diamonds are aspessed 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.] Data Set Diamonds SO.... Sample Variablei - 5 Diamonds Obierations = 308 Diamond Wright Color CLANET Certification Body Price carats Singapore $ 7 Variables GIA GIA Observations GLA GLA 1.641 GLA .595 V51 GLA 1,427 Variable 0.31 GLA 1,427 Variable 0.3 1, 125 1,135 Variable CIA Variable Correlation Correlation MacBook ProDefine population 1 as diamonds certified by GIA and population 2 as diamonds certified by IGI. Similarly, define wj as the mean price of diamonds certified by GIA and up as the mean price of diamonds certified by IGI. The point estimate of HI - H2 is . (Hint: Use the DataView tool to obtain the statistics that form the point estimate.) Distribution AAA -5 -2 The population standard deviations oj and oz are unknown. Use the Distributions tool and the DataView tool to develop a 90% confidence Interval estimate of the difference between the mean prices of diamonds certified by the two certifiers. The 90% confidence interval estimate of the difference between the two population means is LCL = to UCL = 7 . (Hint: The appropriate degrees of freedom is 214.) Based on your interval estimate, a two-tailed hypothesis test of Ho : Hi - #2 = 0 conducted at the 0.10 level of significance would Ho , because the value 0 is In the 90% confidence interval estimate of #1 = #2 .The 90% confidence interval estimate of the difference between the two population means is LCL to UCL - 7 . (Hint: The appropriate degrees of freedom is 214.) Based on your interval estimate, a two-tailed hypothesis test of Ho : #1 - uz = 0 conducted at the 0.10 level of significance would Ho , because the value O is In the 90% confidence interval estimate of Hi - H2 - Maybe consumers don't perceive GIA to be stricter in its grading than IGI. It might be the case that prices of diamonds certified by the two certifiers are different because GIA certifies more large diamonds (which sell for higher prices than small diamonds) than IGI. Now redefine uj as the mean weight of diamonds certified by GIA and ja as the mean weight of diamonds certified by IGI. Using a significance level of a = 0.10, conduct a hypothesis test to determine whether diamonds certified by GIA have a higher mean weight than diamonds certified by IGI. The appropriate degrees of freedom is 174. Again, g, and g2 are unknown, and you can assume that they are unequal. You conduct test with the null and alternative hypotheses formulated as: O Ho : HI - H2 = 0; HI : HI - 12 0 O Ho : HI - H2 = 0; HI : HI - H2 = 0 O Ho : HI - H2 = 0; HI : HI - H2 0 The value of the test statistic is The p-value is . Therefore, you conclude that diamonds certified by GIA have a higher mean weight than diamonds certified by IGI. Grade It Now Save & Continue Continue without saving MacBook Pro