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Answer:
The 94% 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=25 represent the sample 1 size
n2=36 represent the sample 2 size
sample standard deviation for sample 1
sample standard deviation for sample 2
parameter of interest.
The confidence interval for the difference of means is given by the following formula:
(1)
The point of estimate for is just given by:
Since the Confidence is 0.94 or 94%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".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 94% confidence interval would be given by
Answer:
C.
General Formulas and Concepts:
<u>Calculus</u>
- Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that
- MVT is also Average Value
Step-by-step explanation:
<u>Step 1: Define</u>
f'(c) = 20
Interval [1, b]
<u>Step 2: Check/Identify</u>
Function [1, b] is continuous.
Derivative [1, b] is continuous.
∴ There exists a c∈[1, b] such that
<u>Step 3: Mean Value Theorem</u>
- Substitute:
- Rewrite:
And we have our final answer!