The line equation is given by
where <em>m </em>is the slope and <em>b </em>is the interception with <em>Y-axis</em>
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1 answer:
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Answer:
Critical values:
95% confidence interval would be given by (3.646;4.472)
Step-by-step explanation:
1) 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".
The data is:
4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87
2) Compute the sample mean and sample standard deviation.
In order to calculate the mean and the sample deviation we need to have on mind the following formulas:
=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)
On this case the average is
=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)
The sample standard deviation obtained was s=0.6503
3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints
In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=T.INV(0.025,11)" for
"=T.INV(1-0.025,11)" for
The confidence interval for the mean is given by the following formula:
And we can use Excel to calculate the limits for the interval
Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646
Upper interval : "=4.059 +2.201*(0.6503/SQRT(12))" =4.472
So the 95% confidence interval would be given by (3.646;4.472)
Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.
The distances:
- from perihelion to the sun in terms of ellipse is a-c;
- from aphelion to the sun in terms of ellipse is a+c.
Then
Add these two equations:
and subtract first equation from the second:
Note that thus
The equation for the planet's orbit is
Answer: B. No
Step-by-step explanation:
Direct variation has the following form:
Where the constant of variation is "k".
By definition, in direct variation, when the variable "x" changes, tha variable "y" changes in proportion to the variable "x".
As you can observe in the table, when the value of the variable "x" increase, the values of the variable "y" decrease, therefore we can conclude that it is not a direct variation.
Then the answer is the option B.