In 2000, the population of a city was about 15 million, and it was growing by about 3% per year. At this growth rate, the functi
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Answer:
Since is a bilateral test the p value would be:
So the p value is a very high value and using any significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the means are similar for both groups
Step-by-step explanation:
Data given and notation
1:[71 68 50 84 76 76 80 79]
2:[76 63 54 80 79 82 75 82]
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 for both groups are equal , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the samples both are less 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.
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
Calculate the statistic
We can replace in formula (1) the results obtained like this:
Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test. 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 high value and using any significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the means are similar for both groups