Answer:
a) For this case we need to use a t distribution since we know the information about a sample and we don't know the population deviation.
b)
So on this case the 90% confidence interval would be given by (118.904;133.096)
c) For this case since confidence interval include tha value of 130 so then we don't have enough evidence to conclude that the claim by the consultant is incorrect.
Step-by-step explanation:
Part a
For this case we need to use a t distribution since we know the information about a sample and we don't know the population deviation.
Part b
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.
represent the sample mean
population mean (variable of interest)
s=15 represent the sample standard deviation
n=14 represent the sample size
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.90 or 90%, 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(0.05,13)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (118.904;133.096)
Part c
For this case since confidence interval include tha value of 130 so then we don't have enough evidence to conclude that the claim by the consultant is incorrect.
