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Answer:
Since is a bilateral test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the sample mean for Atlanta
represent the sample mean for Chicago
represent the sample deviation for Atlanta
represent the sample standard deviation for Chicago
sample size for the group Atlanta
sample size for the group Chicago
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, 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 value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
The degrees of freedom are given by:
Since is a bilateral test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.