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3. Students looked at the effect of a certain fertilizer on plant growth. The students tested this fertilizer on one group of plants (Group A) and did not give fertilizer to a second group (Group B). Let X and Y denote the respective growths of the plants (in mm) in Group A and Group B over six weeks. Suppose X and Y are independent random variables with distributions N(ux, o) and N(uy, of), respectively. A random sample from N(ux.o) of size n = 25 yielded i 35.83 and s 23.81, while a random sample from N(uy, of) of size m 29 yielded y = 31.51 and s= 33.76. (a) Assume of = o, test the null hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (b) If o + o3, test the null hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (c) Test Ho: o = až against H : ok + ož at the a = 0.05 significance level.

3. Students looked at the effect of a certain fertilizer on plant growth. The students tested this fertilizer on one group of plants (Group A) and did not give fertilizer to a second group (Group B). Let X and Y denote the respective growths of the plants (in mm) in Group A and Group B over six weeks. Suppose X and Y are independent random variables with distributions N(ux, o) and N(uy, of), respectively. A random sample from N(ux.o) of size n = 25 yielded i 35.83 and s 23.81, while a random sample from N(uy, of) of size m 29 yielded y = 31.51 and s= 33.76. (a) Assume of = o, test the null hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (b) If o + o3, test the null hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (c) Test Ho: o = až against H : ok + ož at the a = 0.05 significance level.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. Students looked at the effect of a certain fertilizer on plant growth. The students tested this fertilizer on one group of plants (Group A) and did not give fertilizer to a second group (Group B). Let X and Y denote the respective growths of the plants (in mm) in Group A and Group B over six weeks. Suppose X and Y are independent random variables with distributions N(ux, o) and N(uy, o), respectively. A random sample from N(ux.o%) of size n = 25 yielded i 35.83 and s = 23.81, while a random %3! sample from N(uy o) of size m = 29 yielded y = 31.51 and s = 33.76. %3D (a) Assume o = o, test the null hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (b) If o #o, test the mull hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (c) Test Ho : o = oỷ against H1 : of + oỷ at the a = 0.05 significance level.
Transcribed Image Text:3. Students looked at the effect of a certain fertilizer on plant growth. The students tested this fertilizer on one group of plants (Group A) and did not give fertilizer to a second group (Group B). Let X and Y denote the respective growths of the plants (in mm) in Group A and Group B over six weeks. Suppose X and Y are independent random variables with distributions N(ux, o) and N(uy, o), respectively. A random sample from N(ux.o%) of size n = 25 yielded i 35.83 and s = 23.81, while a random %3! sample from N(uy o) of size m = 29 yielded y = 31.51 and s = 33.76. %3D (a) Assume o = o, test the null hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (b) If o #o, test the mull hypothesis at 1% significance level that the mean growths are equal against the alternative that the fertilizer enhanced growth. (c) Test Ho : o = oỷ against H1 : of + oỷ at the a = 0.05 significance level.
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