Listed below are heights in meters of trees included in an experiment. a) constr

Question

Listed below are heights in meters of trees included in an experiment. a) construct a 95% confidence interval estimate of the mean height for the population of control group trees. b) construct a 95% confidence interval estimate of the mean height for the population of trees given the irrigation treatment. c) compare results (please show the steps so I can understand how you guys get the answer!!)
control group: 3.2, 1.9, 3.6, 4.6, 4.1, 5.1, 5.5, 4.8, 2.9, 4.9, 3.9, 6.9, 6.8, 6.0, 6.9, 6.5, 5.5, 5.5, 4.1, 6.3
irrigation treatment: 4.1, 2.5, 4.5, 3.6, 2.8, 5.1, 2.9, 5.1, 1.2, 1.6, 6.4, 6.8, 6.5, 6.8, 5.8, 2.9, 5.5, 3.3, 6.1, 6.1

Explanation / Answer

a) construct a 95% confidence interval estimate of the mean height for the population of control group trees.

Mean height for the population of control group trees Xcontrol - bar = sum of all number/20 = 4.95 meter

Standard error for the population of control group trees scontrol-bar = 1.421 meter [ calculate it by standard formula]

95% confidence interval = Xcontrol - bar +- t* (scontrol-bar/n)

t* = tcritical for dF = 20-1 = 19 and alpha = (1-0.95)/2 = 0.025

so  tcritical = +-2.093

95% confidence interval = Xcontrol - bar +- t* (scontrol-bar/n) = 4.95 +- 2.093 * (1.421/20)

= (4.285, 5.615)

b) construct a 95% confidence interval estimate of the mean height for the population of trees given the irrigation treatment.

Mean height for the population of irrigation treatment group trees Xirrigation = sum of all numbers/20 = 4.48 meter

Standard error for the population of irrigation treatment group trees sirrigation-bar = 1.7834 meter [calculate it by standard formula]

95% confidence interval = Xirrigtion - bar +- t* (sirrigation-bar/n)

t* = tcritical for dF = 20-1 = 19 and alpha = (1-0.95)/2 = 0.025

so  tcritical = +-2.093

95% confidence interval = Xirrigation - bar +- t* (sirrigation-bar/n) = 4.48 +- 2.093 * (1.7834/20)

= (3.645, 5.315)

(c) 95% confidence interval estimate of the mean height for the population of control group trees. =(4.285, 5.615)

95% confidence interval estimate of the mean height for the population of trees given the irrigation treatment. = (3.645, 5.315)

Both confidence intervals intersect with each other so there is no significant difference between mean height for both type of groups.

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