Please also show how to solve for the standard error of mean (difference) manual

Question

Please also show how to solve for the standard error of mean (difference) manually. Thanks 4. The hindleg length (cm) and foreleg length (cm) are measured on each of ten randomly chosen deer brought to a check point during hunting season, with the following results: Deer Hindleg length Foreleg length 142 138 140 136 147 144 144 139 142 143 141 146 143 149 145 150 136 142 146 148 10 Test the null hypothesis that the mean hindleg length and the mean foreleg length are the same in the population of deer from which this sample was obtained.

Explanation / Answer

We have to test the null hypothesis H0: µd= versus the alternative Ha: µd0

Here µd is the true mean of difference in hindleg and foreleg length respectively.

Degree of freedom =n-1=10-1=9

At 5% level two tailed critical t=2.262

Calculated t from following results is t(9)=3.41

As calculated t>2.262 , we reject the null hypothesis and as t is positve we conclude that hindleg length is larger than the foreleg length.

Standard error of mean =s/sqrt(n)=3.057/sqrt(10)=0.9667

Paired T-Test and CI: Hindleg Length, Foreleg Length

Paired T for Hindleg Length - Foreleg Length

N Mean StDev SE Mean
Hindleg Length 10 144.70 3.40 1.08
Foreleg Length 10 141.40 4.03 1.28
Difference 10 3.300 3.057 0.967

95% CI for mean difference: (1.113, 5.487)
T-Test of mean difference = 0 (vs 0): T-Value = 3.41 P-Value = 0.008

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