A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample m
1 answer:
Answer:
0.5
Step-by-step explanation:
Solution:-
- The sample mean before treatment, μ1 = 46
- The sample mean after treatment, μ2 = 48
- The sample standard deviation σ = √16 = 4
- For the independent samples T-test, Cohen's d is determined by calculating the mean difference between your two groups, and then dividing the result by the pooled standard deviation.
Cohen's d =
- Where, the pooled standard deviation (sd_pooled) is calculated using the formula:
- Assuming that population standard deviation and sample standard deviation are same:
SD_1 = SD_2 = σ = 4
- Then,
- The cohen's d can now be evaliated:
Cohen's d =
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Answer:
And rounded up we have that n=2663
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".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume an estimated proportion of since we don't have prior info provided. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=2663
See the attached picture.
- Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
The resulting box has a volume
because the volume of a box is the product of its width , length
, and height
.
- find the zeroes
You know right away from the factored form of that the zeroes are
. (zero product property)
- sketch the graph of the function
Easy to plot by hand. You know the zeroes, and you can check the sign of for any values of
between these zeros to get an idea of what the graph of
looks like. See the second attached picture.
Here's what I mean by "check the sign" in case you don't follow. We know when
and
. So we pick some value of
between them, say
, and find that
which is positive, so will be positive for any other
between 0 and 8. Similarly we would find that
for
between 8 and 12, and so on.
- What is the size of the cutout he needs to make so that he can fit the most marbles in the box?
It's impossible to answer this without knowing the volume of each marble...
- If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?
Thomas wants , so you solve
While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions
but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.
- What would be the dimensions of this box?
The box's dimensions are ( in) x (
in) x (
in).
If , then
and
.
If , then
and
.
