Answer:
a) The 95% confidence interval would be given by
b) No contradict the result obtained since the confidence interval contains the value 0, so we don't have enough evidence to conclude that we have a significant effect in the colling rate and the hardness.
Step-by-step explanation:
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=50 represent the sample 1 size
n2=40 represent the sample 2 size
sample standard deviation for sample 1
sample standard deviation for sample 2
parameter of interest.
Part a
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(0.025,88)".And we see that
The standard error is given by the following formula:
And replacing we have:
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by
Part b
No contradict the result obtained since the confidence interval contains the value 0, so we don't have enough evidence to conclude that we have a significant effect in the colling rate and the hardness.