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Answer:
a)
So on this case the 95% confidence interval would be given by (179.032;186.968)
b)
So on this case the 95% confidence interval would be given by (185.437;194.563)
c) For Summer the confidence interval was (179.032;186.968) and as we can see our upper limit is <190 so then we can conclude that they are below the specification of 190 at 5% of significance
For Winter the confidence interval was (185.437;194.563) and again the upper limit is <190 so then we can conclude that they are below the specification of 195 at 5% of significance
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 for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Part a : Summer
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 0.95 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(0.025,99)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (179.032;186.968)
Part b: Winter
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 0.95 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(0.025,99)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (185.437;194.563)
Part c
For Summer the confidence interval was (179.032;186.968) and as we can see our upper limit is <190 so then we can conclude that they are below the specification of 190 at 5% of significance
For Winter the confidence interval was (185.437;194.563) and again the upper limit is <190 so then we can conclude that they are below the specification of 195 at 5% of significance
The attached graph represents the graph of f(x) = (x - 1)^2 - 2
<h3>How to plot the graph?</h3>The equation is given as:
f(x) = (x - 1)^2 - 2
Next, we set x to -2, -1, 0, 1 and 2.
So, we have:
f(-2) = (-2 - 1)^2 - 2 = 7
f(-1) = (-1 - 1)^2 - 2 = 2
f(0) = (0 - 1)^2 - 2 = -1
f(1) = (1 - 1)^2 - 2 = -2
f(2) = (2 - 1)^2 - 2 = -1
This means that the table of values is
x f(x)
-2 7
-1 2
0 -1
1 -2
2 -1
Next, we plot the above points and connect them.
See attachment for the graph of f(x) = (x - 1)^2 - 2
Read more about graphs and functions at:
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