3. Take the mean and standard deviation of data set A calculated in problem 1 an

Question

3. Take the mean and standard deviation of data set A calculated in problem 1 and assume that they are population parameters (? and ?) known for the variable fish length in a population of rainbow trouts in the Coldwater River. Imagine that data set B is a sample obtained from a different population in Red River (Chapter 6 problem!). a) Conduct a hypothesis test to see if the mean fish length in the Red River population is different from the population in Coldwater River. b) Conduct a hypothesis test to see if the variance in fish length is different in the Red River population compared to the variance in the Coldwater population

Explanation / Answer

a] Two-Sample T-Test

Two-sample T for set A vs set B

N Mean StDev SE Mean
set A 11 60.378 0.446 0.13
set B 8 60.872 0.419 0.15

Difference = ? (set A) - ? (set B)
Estimate for difference: 0.494

To test hypothesis,

H0: ? (set B) =  ? (set A) Vs H1:  ? (set B) is not equal to  ? (set A)
T-Test of difference = 0 (vs ?): T-Value = 2.47 P-Value = 0.026 DF = 15

Here pvalue = 0.026 < alpha = 0.05

therefore we reject H0 at 5 % los. Mean fish length in red river population is different from the population in coldwater river.

b]  Test for Two Variances: set A, set B

Method

Null hypothesis ?(set A) = ?(set B)
Alternative hypothesis ?(set A) ? ?(set B)
Significance level ? = 0.05

Statistics

Variable N StDev Variance
set A 11 0.446 0.199  
set B 8 0.419 0.176

Ratio of standard deviations = 1.063
Ratio of variances = 1.130

P value = 0.4478 > alpha = 0.05

Accept H0.

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