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Answer:
So the p value is a very low value and using any significance level for given always
so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that the two means are significantly different at 5%
Step-by-step explanation:
Data given and notation
represent the mean for the sample 1
represent the mean for the sample 2
represent the sample standard deviation for the sample 1
represent the sample standard deviation for the sample 2
sample size for the group 1
sample size for the group 2
t would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the mean are different , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the samples both are higher than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-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
We can replace in formula (1) the results obtained like this:
Statistical decision
The first step is calculate the degrees of freedom, on this case:
Since is a bilateral test the p value would be:
So the p value is a very low value and using any significance level for given always
so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that the two means are significantly different at 5%