Suppose you want to determine whether the average values for populations 1 and 2

Question

Suppose you want to determine whether the average values for populations 1 and 2 are different, and you randomly gather the following data. Test your conjecture, using a probability of committing a Type I error of .01. Assume the population variances are the same and X is normally distributed in the populations.

Find the t-score to make a conclusion.

Round the answer to two decimal places.

Observed t = ()

fail to reject the null hypothesis

.

The tolerance is +/- 0.05.

Sample 1 Sample 2 2 10 7 8 2 5 10 12 8 7 9 11 9 1 8 0 2 8 9 8 9 10 11 10 11 2 4 5 3 9 11 10 7 8 10 10

Explanation / Answer

from above pooled std deviation Sp =((n1-1)s12+(n2-1)s22)/(n1+n2-2))1/2 =2.6482

hence std error =(Sp(1/n1+1/n2)1/2) =0.8827

also X1-X2 =-4.1

hence test stat =(X1-X2)/std error =4.429

here degree of freedom =n1+n2-2 =18+18-2 =34

for 34 degree of freedom and above t stat p value ~ 0.0000

as p value is less then 0.01 level , we reject the null hypothesis, that mean are equal/

S. no sample 1 sample 2 1 2 10 2 10 12 3 7 8 4 8 7 5 2 9 6 5 11 7 9 9 8 1 8 9 8 9 10 0 10 11 2 11 12 8 10 13 11 11 14 2 10 15 4 7 16 5 8 17 3 10 18 9 10 total 96.000 170.000 mean 5.333 9.444 std deviation(S) 3.464 1.423

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