A research study investigated the composition of wines from the Rhine and Moselle wine regions of Germany. One component measured was the concentration of i-Butyl alcohol. The results of the study are listed in the following table: Region n i-Butyl alcohol (mg/100ml) Rhine 9 ̄x =5.32,s =2.24 Moselle 14 ̄x =3.62,s =0.97 (a) Assume that the underlying population variances from the two regions are identical. At the 0.05 level of significance, test the null hypothesis that the mean concentration of i-Butyl alcohol is the same for wines from the Rhine and Moselle regions. Construct a 95% confidence interval (b) Now assume that the underlying population variances from the two regions differ. At the 0.05 level of significance, test the null hypothesis that the mean concentration of i-Butyl alcohol is the same for wines from the Rhine and Moselle regions, construct a 95% confidence interval (c) If you were to provide a report to the investigators which of the above results would you include and why?
A research study investigated the composition of wines from the Rhine and Moselle wine regions
of Germany. One component measured was the concentration of i-Butyl alcohol. The results of
the study are listed in the following table:
Region n i-Butyl alcohol (mg/100ml)
Rhine 9 ̄x =5.32,s =2.24
Moselle 14 ̄x =3.62,s =0.97
(a) Assume that the underlying population variances from the two regions are identical. At the
0.05 level of significance, test the null hypothesis that the
alcohol is the same for wines from the Rhine and Moselle regions.
Construct a 95% confidence interval
(b) Now assume that the underlying population variances from the two regions differ. At the 0.05
level of significance, test the null hypothesis that the mean concentration of i-Butyl alcohol is
the same for wines from the Rhine and Moselle regions, construct a 95% confidence interval
(c) If you were to provide a report to the investigators which of the above results would you
include and why?
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