20 POINTS)
1 answer:
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Answer:
Step-by-step explanation:
Data given and notation
represent the mean for the sample 1
represent the mean for the sample 2
represent the population standard deviation for the sample 1
represent the population standard deviation for the sample 2
sample size for the group 1
sample size for the group 2
z would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:
H0:
H1:
If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:
(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:
And with this we can replace in formula (1) like this: