3. The following histograms show two samples with replace- ment from two populat

Question

3. The following histograms show two samples with replace- ment from two populations. The top histogram shows the data sampled from the first population (based on n-120 samples). The bottom histogram shows the data sampled from the second population (based on n2 100 samples) Is the data consistent or contradictory to the statement that the two populations the same mean? Hint: just by looking at the histograms you should be able to get a good idea of the values of X1 and X2 (i.e. the averages of the two samples, respectively) and ?1 and ?2 (where ?1, ?2 denote the two population variances, respectively), then figure out the approximate value of the z-score for testing that the two populations have the same mean using the fact that 1-/ 2/-120 100 120-f 100. 6 7

Explanation / Answer

From both the histograms, roughly we can see that the values are:

Mean (1) = -0.2

Standard Deviation (1) = 0.8

Mean (2) = 1.2

SD (2) = 1

Now, performing a two-sample independent z-test:

Here, the denominator: sqrt(0.64/120 + 1/100) = 0.12

u1 - u2 = 0

x1 - x2 = -1.4

z-score = -1.4/0.12 = 11.67

Hence, 11.67 is the approximate value of z-score (more than critical value)

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