In a study to compare two different corrosion inhibitors, specimens of stainless steel were immersed for four hours in a solution containing sulfuric acid and a corrosion inhibitor. Forty-seven specimens in the presence of inhibitor A had a mean weight loss of 242 mg and a standard deviation of 20 mg, and 42 specimens in the presence of inhibitor B had a mean weight loss of 220 mg and a standard deviation of 31 mg. Find a 95% confidence interval for the difference in m

And the confidence interval for the difference of means is given by:

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data given and notation

represent the mean for the sample A

represent the mean for the sample B

represent the sample standard deviation for the sample A

represent the sample standard deviation for the sample B

sample size selected A

sample size selected B

represent the significance level

Confidence =0.95 or 95%

Solution to the problem

For this case the confidence interval for the difference of means is given by:

The degrees of freedom are given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,87)".And we see that

And the confidence interval would be given by

And the confidence interval for the difference of means is given by:

the answer

b. they are parallel and will never intersect.