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Answer:
The 95% confidence interval for the difference between means is (-2164.21, -299.13).
The lower limit on the confidence interval is -$2164.21.
The upper limit on the confidence interval is -$299.13.
Step-by-step explanation:
The sample data is:
Gender Mean Std. dev. n
Female 2577.75 1916.29 67
Male 3809.42 2379.47 33
We have to calculate a 95% confidence interval for the difference between means, with a T-model.
The sample 1, of size n1=67 has a mean of 2577.75 and a standard deviation of 1916.29.
The sample 2, of size n2=33 has a mean of 3809.42 and a standard deviation of 2379.47.
The difference between sample means is Md=-1231.67.
The estimated standard error of the difference between means is computed using the formula:
The t-value for a 95% confidence interval is t=1.96.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference between means is (-2164.21, -299.13).