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3.13 Consider the following estimated area response model for sugar cane (area of sugar cane planted in thousands of hectares in a region of Bangladesh), as a function of relative price (100 times the price of sugar cane divided by the price of jute, which is an alternative crop to sugar cane, planted by Bangladesh farmers), AREA, = -0.24+0.50RPRICE, using 34 annual observations. a. The sample average of RPRICE is 114.03, with a minimum of 74.9 and a maximum of 182.2. RPRICE is the price of sugar cane taken as a percentage of the price of jute. What do these sample statistics tell us about the relative price of sugar cane? b. Interpret the intercept and slope of the estimated relation. c. The t-statistic is -0.01 for the hypothesis that the intercept parameter is zero. What do you con- clude? Is this an economically surprising result? Explain. d. The sample mean area planted is 56.83 thousand hectares, and the sample mean for relative price is 114.03. Taking these values as given, test at the 5% level of significance the hypothesis that the elasticity of area response to price at the means is 1.0. The estimated variance of the coefficient of RPRICE is 0.020346. e. The model is re-estimated in log-linear form, obtaining In (AREA,) = 3.21 +0.0068RPRICE.. Interpret the coefficient of RPRICE. The standard error of the slope estimate is 0.00229. What does that tell us about the estimated relationship? f. Using the model in (e), test the null hypothesis that a 1% increase in the price of sugar cane relative to the price of jute increases the area planted in sugar cane by 1%. Use the 5% level of significance and a two-tail test. Include (i) the test statistic and its distribution if the null hypothesis is true, (ii) a sketch of the rejection region, (iii) show the location of the test statistic value, (iv) state your conclusion, and (v) show on the sketch, the region that would represent the p-value. atistic in

3.13 Consider the following estimated area response model for sugar cane (area of sugar cane planted in thousands of hectares in a region of Bangladesh), as a function of relative price (100 times the price of sugar cane divided by the price of jute, which is an alternative crop to sugar cane, planted by Bangladesh farmers), AREA, = -0.24+0.50RPRICE, using 34 annual observations. a. The sample average of RPRICE is 114.03, with a minimum of 74.9 and a maximum of 182.2. RPRICE is the price of sugar cane taken as a percentage of the price of jute. What do these sample statistics tell us about the relative price of sugar cane? b. Interpret the intercept and slope of the estimated relation. c. The t-statistic is -0.01 for the hypothesis that the intercept parameter is zero. What do you con- clude? Is this an economically surprising result? Explain. d. The sample mean area planted is 56.83 thousand hectares, and the sample mean for relative price is 114.03. Taking these values as given, test at the 5% level of significance the hypothesis that the elasticity of area response to price at the means is 1.0. The estimated variance of the coefficient of RPRICE is 0.020346. e. The model is re-estimated in log-linear form, obtaining In (AREA,) = 3.21 +0.0068RPRICE.. Interpret the coefficient of RPRICE. The standard error of the slope estimate is 0.00229. What does that tell us about the estimated relationship? f. Using the model in (e), test the null hypothesis that a 1% increase in the price of sugar cane relative to the price of jute increases the area planted in sugar cane by 1%. Use the 5% level of significance and a two-tail test. Include (i) the test statistic and its distribution if the null hypothesis is true, (ii) a sketch of the rejection region, (iii) show the location of the test statistic value, (iv) state your conclusion, and (v) show on the sketch, the region that would represent the p-value. atistic in

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Please solve 3.13 in its entirety, thanks!
d f 그 C ypothesis Ho Y2 -0.02 against the alternative H₁:12 < -0.02 using the a = 0.01 level of significance. Include in your answer (i) the test statistic and its distribution if the null hypothesis is true, (ii) a sketch of the rejection region, (iii) show the location of the test Po statistic value, (iv) state your conclusion, and (v) show on the sketch the region that would represent the p-value. nowe. "Hypothesis tests and interval estimators for the regression model are valid as long as the regression error terms are normally distributed." Is this true or false? Explain. 3.13 Consider the following estimated area response model for sugar cane (area of sugar cane planted in thousands of hectares in a region of Bangladesh), as a function of relative price (100 times the price of sugar cane divided by the price of jute, which is an alternative crop to sugar cane, planted by Bangladesh farmers), AREA, = -0.24 +0.50RPRICE, using 34 annual observations. basa. The sample average of RPRICE is 114.03, with a minimum of 74.9 and a maximum of 182.2. adt ad RPRICE is the price of sugar cane taken as a percentage of the price of jute. What do these sample ad ost statistics tell us about the relative price of sugar cane? b. Interpret the intercept and slope of the estimated relation. c. The t-statistic is -0.01 for the hypothesis that the intercept parameter is zero. What do you con- clude? Is this an economically surprising result? Explain. d. The sample mean area planted is 56.83 thousand hectares, and the sample mean for relative price is 114.03. Taking these values as given, test at the 5% level of significance the hypothesis that the elasticity of area response to price at the means is 1.0. The estimated variance of the coefficient of RPRICE is 0.020346. e. The model is re-estimated in log-linear form, obtaining In (AREA,) = 3.21 +0.0068RPRICE. Interpret the coefficient of RPRICE. The standard error of the slope estimate is 0.00229. What does that tell us about the estimated relationship? f. Using the model in (e), test the null hypothesis that a 1% increase in the price of sugar cane relative to the price of jute increases the area planted in sugar cane by 1%. Use the 5% level of significance and a two-tail test. Include (i) the test statistic and its distribution if the null hypothesis is true, (ii) a sketch of the rejection region, (iii) show the location of the test statistic value, (iv) state your conclusion, and (v) show on the sketch, the region that would represent the p-value. 3.14 What is the meaning of statistical significance and how valuable is this concept? A t-statistic is t=(b-c)/se(b), where b is an estimate of a parameter ß, c is the hypothesized value, and se(b) is lavy the standard error. If the sample size N is large, then the statistic is approximately a standard normal distribution if the null hypothesis ß= c is true. a. With a 5% level of significance, we assert that an event happening with less than a one in 20 itinallu cignificant " while an event happening with more than a one in 20 chance is
Transcribed Image Text:d f 그 C ypothesis Ho Y2 -0.02 against the alternative H₁:12 < -0.02 using the a = 0.01 level of significance. Include in your answer (i) the test statistic and its distribution if the null hypothesis is true, (ii) a sketch of the rejection region, (iii) show the location of the test Po statistic value, (iv) state your conclusion, and (v) show on the sketch the region that would represent the p-value. nowe. "Hypothesis tests and interval estimators for the regression model are valid as long as the regression error terms are normally distributed." Is this true or false? Explain. 3.13 Consider the following estimated area response model for sugar cane (area of sugar cane planted in thousands of hectares in a region of Bangladesh), as a function of relative price (100 times the price of sugar cane divided by the price of jute, which is an alternative crop to sugar cane, planted by Bangladesh farmers), AREA, = -0.24 +0.50RPRICE, using 34 annual observations. basa. The sample average of RPRICE is 114.03, with a minimum of 74.9 and a maximum of 182.2. adt ad RPRICE is the price of sugar cane taken as a percentage of the price of jute. What do these sample ad ost statistics tell us about the relative price of sugar cane? b. Interpret the intercept and slope of the estimated relation. c. The t-statistic is -0.01 for the hypothesis that the intercept parameter is zero. What do you con- clude? Is this an economically surprising result? Explain. d. The sample mean area planted is 56.83 thousand hectares, and the sample mean for relative price is 114.03. Taking these values as given, test at the 5% level of significance the hypothesis that the elasticity of area response to price at the means is 1.0. The estimated variance of the coefficient of RPRICE is 0.020346. e. The model is re-estimated in log-linear form, obtaining In (AREA,) = 3.21 +0.0068RPRICE. Interpret the coefficient of RPRICE. The standard error of the slope estimate is 0.00229. What does that tell us about the estimated relationship? f. Using the model in (e), test the null hypothesis that a 1% increase in the price of sugar cane relative to the price of jute increases the area planted in sugar cane by 1%. Use the 5% level of significance and a two-tail test. Include (i) the test statistic and its distribution if the null hypothesis is true, (ii) a sketch of the rejection region, (iii) show the location of the test statistic value, (iv) state your conclusion, and (v) show on the sketch, the region that would represent the p-value. 3.14 What is the meaning of statistical significance and how valuable is this concept? A t-statistic is t=(b-c)/se(b), where b is an estimate of a parameter ß, c is the hypothesized value, and se(b) is lavy the standard error. If the sample size N is large, then the statistic is approximately a standard normal distribution if the null hypothesis ß= c is true. a. With a 5% level of significance, we assert that an event happening with less than a one in 20 itinallu cignificant " while an event happening with more than a one in 20 chance is
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