You'll need to start by finding a 95% confidence interval for 2 samples. If you use a z-table, then here is an example of a formula:
CI95 = (x1 - x2) ± 1.96 [√(s1^2/n1 + s2^2/n2)]
...where x1, x2 are the means; ± 1.96 represents the 95% confidence interval using a z-table; s1, s2 are the standard deviations (^2 means squared); and n1, n2 are the sample sizes.
Plug the values from your problem into the formula and determine the interval.
I hope this brief explanation will help get you started.
A company has two factories in which they manufacture engines. Once a month they randomly select 10 engines from each factory and test if there is a difference in performance in engines made in the two factories. This month the average output of the motors from Factory 1 is 120 horsepower with a standard deviation of 5 horsepower, and the average output of the motors from Factory 2 is 132 horsepower with a standard deviation of 4 horsepower.
(a) Calculate a 95% confidence interval for the difference in the average horsepower for engines coming from the two factories and interpret it in context.
(b) Based on your confidence interval, is there a significant evidence that there is a dif- ference in performance in engines made in the two factories? If so, can you tell which factory produces motors with lower performance? Explain.
(c) Recently upgrades were made in Factory 2. Do these data prove that these upgrades enhanced the performance in engines made in this factory? Explain.
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