Jackie bought a 3-pack of tubes of glue. She used 0.27 ounce of the glue from the 3-pack
2 answers:
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Answer:
A and C
Step-by-step explanation:
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.
And in order to conduct it we need to have some assumptions:
1) The dependent variable must be continuous (interval/ratio).
2) The observations are independent of one another.
3) The dependent variable should be approximately normally distributed.
4) The dependent variable should not contain any outliers.
Let's analyze one by one the options on this case:
A. The methods used to evaluate the mean of the differences between two dependent variables apply if one has 86 IQ scores of taxpayers from Texas and 86 IQ scores of taxpayers from Ohio
We can assume that is true since the two variables are dependent and we are assuming that all the other conditions are satisfied to use the t paired test.
B. The requirement of a simple random sample is satisfied if we have matched pairs of voluntary response data.
That's not neccesary true since is not a requirement in order to use the t pairedtest.
C. If one has more than 23 matched pairs of sample data, one can consider the sample to be large and there is no need to check for normality.
We can assume that is true since we need to ensure normality in order to apply the test and if the sample size is large enough large we can apply the test.
D. If one has twenty matched pairs of sample data, there is a loose requirement that the twenty differences appear to be from a normally distributed population.
False the requirement of normality is important to apply the test not a loose requirement.
E. If one wants to use a confidence interval to test the claim that mu Subscript d Baseline greater than 0 with a 0.01 significance level, the confidence interval should have a confidence level of 98%.
That's not correct the significance level is and that not correspond to the significance level given on this case.
The given dimensions of the base of the box are 2 x 3 units.
Let h be the height of the box.
So, the volume of the box = 2 x 3 x h ...(i)
The shape of baseball is spherical and one baseball fits in a cubical box having the minimum dimensions equal to the diameter of the spherical ball.
Assuming the diameter of the baseball is d units.
So, the volume occupied by one baseball= volume of the cubical box having the side units.
cubic units
So, the volume required to pack 48 baseballs
Assuming that all the baseballs fit in the box, i.e peripheral balls in every horizontal and vertical layer touched the box as shown in the figure.
So, the length, 3 units and the width, 2 units, must be the integral multiple of the diameter, units, of the baseball. i.e
The length,
The width,
The height,
where and
belong to the natural number.
This required volume must be equals to the volume of the box.
From equations (i) and (ii),
[from (iii) and (iv)]
On comparing with the equation (iv)
Now, if the diameter of the baseball is unity,i.e, d=1 unit
( integer) and (integer) [from (iii) and (iv)]
(also an integer) [from (v)]
Now, the height of the box,
unit.
Hence, the other dimension of the box, is 8 units corrosponding to the unity diameter of the baseball.
Note the height of the box depends on the diameter of the baseball, so it will have infinite possible value for different value of the diameter.
For example, the value of height for d=1 unit has been shown.
and another example may be if units, then (integer) and (integer)
(also an integer) [from (v)]
Now, the height of the box,
unit. [from (iv)]
Here, the height of the box is 2 units corrosponding to 0.5 unit diameter of the baseball.
The possivle values of d can be taken for which and
must be integers.
