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Examination #1

# Examination #1 - Gregory Smith Dr Cuellar Econ 317...

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Gregory Smith 10/9/2009 Dr. Cuellar – Econ 317 Examination #1 Summary Statistics (a) What is the mean price of a bottle of Napa County Cabernet Sauvignon? (a) . su price if Cab==1 & Napa==1 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- price | 14639 34.46724 22.78222 1.8333 232 The mean price of a bottle of Napa County Cabernet Sauvignon is \$34.46724. (b) What is the mean price of a bottle of Sonoma County Cabernet Sauvignon? (a) . su price if Cab==1 & Napa==0 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- price | 9966 18.34801 8.765954 1.5732 72.6667 The mean price of a bottle of Sonoma County Cabernet Sauvignon is \$18.34801.

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0 .02 .04 .06 .08 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Sonoma Napa Density Price Per 750ML Bottle Graphs by Napa=1 (c) Show graphically No they do not look similar. Although both are skewed to the right, the majority of Sonoma bottles are priced ≤ 20 while the majority of Napa bottle prices are ≥20. (d) Set up a hypothesis test to test for a difference in price between Napa and Sonoma County Cabernet Sauvignons. Be sure to clearly state and interpret the null and alternative hypothesis. H : β = 0 This is the null hypothesis. It states that there is not an average price variation large enough to warrant a correlation. There is not a significant price variation between the two products. H : β ≠ 0 This is the alternative hypothesis. This hypothesis states that there is a significant average price difference large enough to account for margin of error and the desired confidence interval. (i) What is considered a statistically significant difference in price using a 5% level of significance? Explain fully and show graphically.
. ttest price if Cab==1, by(Napa) Two-sample t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- Sonoma | 9966 18.34801 .0878089 8.765954 18.17589 18.52014 Napa | 14639 34.46724 .1882957 22.78222 34.09816 34.83632 ---------+-------------------------------------------------------------------- combined | 24605 27.93831 .1279054 20.06321 27.68761 28.18902 ---------+-------------------------------------------------------------------- diff | -16.11923 .2394363 -16.58854 -15.64992 ------------------------------------------------------------------------------ diff = mean(Sonoma) - mean(Napa) t = -67.3216 Ho: diff = 0 degrees of freedom = 24603 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000 . display invttail(24603, .05/2) 1.9600604 . display 1.9600604*.2394363 .46930961 The critical value is .46930961. Anything greater than .46928887 or smaller than -.46928887 is in the rejection region and we would conclude a rejection of the null hypothesis.

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(ii) Compare the actual difference in price between Napa and Sonoma County Cabernet Sauvignon with your answer in (i). Is the difference statistically significant? Explain fully and show graphically. Actual mean difference in price is -16.11923. This is much larger than our critical value and thus we reject the null hypothesis. . display invttail( 24603, .05/2) 1.9600604 (iii) Use a t-test to test for a difference in price between Napa and Sonoma County Cabernet Sauvignon. Explain your results and show graphically. ttest price if Cab==1, by(Napa)
Two-sample t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- Sonoma | 9966 18.34801 .0878089 8.765954 18.17589 18.52014 Napa | 14639 34.46724 .1882957 22.78222 34.09816 34.83632 ---------+-------------------------------------------------------------------- combined | 24605 27.93831 .1279054 20.06321 27.68761 28.18902 ---------+-------------------------------------------------------------------- diff | -16.11923 .2394363 -16.58854 -15.64992 ------------------------------------------------------------------------------ diff = mean(Sonoma) - mean(Napa) t = -67.3216 Ho: diff = 0 degrees of freedom = 24603 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000 Critical t=1.9600604 Actual t = -67.3216 T Statistic (-1.9600604) > -67.3216 Reject the null hypothesis and hold the alternate hypothesis as true.

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Examination #1 - Gregory Smith Dr Cuellar Econ 317...

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