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2 answers:
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Answer:
a)
b) The 90% confidence interval would be given by (63.330;81.070)
Step-by-step explanation:
1) Previous concepts and notation
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".
Let put some notation
x=left arm , y = right arm
x: 175 169 182 146 144
y: 102 101 94 79 79
The first step is define the difference , that is given so we have:
d: 73, 68, 88, 67, 65
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
2) Confidence interval
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(0.05,4)".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 (63.330;81.070)