Suppose we have two independent, normally distributed, populations and we draw a random sample from each population. For population A, we drew a sample of 13 and found the mean to be 17 with a standard deviation of 4. For population B, we drew a sample of 12 with a mean of 19 and a standard deviation of 3. We want to determine if the treatments result in the same effect. Show all work.

Since the calculated value of z=  -1.421 does not lie in the critical region z >

- 1.96 the null hypothesis is accepted and it is concluded that the treatments result in the same effect.

Step-by-step explanation:

1) Let the null and alternate hypothesis be

H0:  μa  − μb = 0  the treatments result in the same effect

against the claim

Ha: μa − μb ≠ 0   the treatments  do not result in the same effect

2) The significance level is set at 0.05

3) The critical region is z =  ± 1.96

4) The test statistic

Z= x1`-x2`/ sqrt [( s1²/n1+ s2²/n2)]

Here

x1`= 17             s1= 4               n1= 13

x2`= 19             s2= 3             n2= 12

5) Calculations

Z= x1`-x2`/ sqrt [( s1²/n1+ s2²/n2)]

z= 17-19/sqrt [( 16/13+ 9/12)]

z= -2/1.40739

z= -1.421

6) Conclusion

Since the calculated value of z=  -1.421 does not lie in the critical region z >

- 1.96 the null hypothesis is accepted and it is concluded that the treatments result in the same effect.

step-by-step explanation: s

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