Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. the data follows: m = 5, x = 114.1, s1 = 5.08, n = 5, y = 129.9, and s2 = 5.37. calculate a 95% ci for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (round your answers to two decimal places.)

The 95% confidence interval would be 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".  

represent the sample mean 1

represent the sample mean 2

n1=5 represent the sample 1 size  

n2=2 represent the sample 2 size  

sample standard deviation for sample 1

sample standard deviation for sample 2

parameter of interest.

Confidence interval

The confidence interval for the difference of means is given by the following formula:  

(1)  

The point of estimate for is just given by:

In order to calculate the critical value we need to find first the degrees of freedom, 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(0.025,8)".And we see that  

The standard error is given by the following formula:

And replacing we have:

Confidence interval

Now we have everything in order to replace into formula (1):  

So on this case the 95% confidence interval would be given by