Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B25%7D%7D%3D%5Cfrac%7B1%7D%7B5%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Width for n = 64:
![\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]](https://tex.z-dn.net/?f=%5Ctext%7BWidth%7D%3D2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7B64%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5B2%5Ccdot%20z_%7B%5Calpha%2F2%7D%5Ccdot%20%5Csigma%5D)
Thus, the sample consisting of 64 data values would give a greater precision
This is something you'll need a T table for, or a calculator that can compute critical T values. Either way, we have n = 10 as our sample size, so df = n-1 = 10-1 = 9 is the degrees of freedom.
If you use a table, look at the row that starts with df = 9. Then look at the column that is labeled "95% confidence"
I show an example below of what I mean.
In that diagram, the row and column mentioned intersect at 2.262 (which is approximate). This value then rounds to 2.26
<h3>
Answer: 2.26</h3>
Answer:
Step-by-step explanation:
Set this up as ratio of vinegar to oil in fraction form:
That's what we're given. If we are looking to find how much oil he needs if he's using 9 ounces of vinegar, then 9 goes on top with the vinegar stuff and x goes on bottom as the unknown amount of oil:
Cross multiply to get
5x = 90 and
x = 18
Which you probably could do without the proportions. If he is using 5 ounces of vinegar and double that amount of oil, then it just makes sense that if he uses 9 ounces of vinegar he will double that amount in oil to use 18 ounces.
The answer would be 64, because 25% is a quarter of 100. That means you would have to multiply 16 by 4.
Answer:
Step-by-step explanation:
Given g (x) = 
and 
, we are to find 
First we need to get 
Hence 
Also given f(x) = x and g(x) = 1/x, we are to find 
For the pair of function f(x) = 2/x and g(x) = 2/x
f(g(x)) = f(2/x)
f(2/x) = 2/(2/x)
f(2/x) = 2*x/2
f(2/x) = x
Hence f(g(x)) = x
For the pair of function f(x) = x-2/3 and g(x) = 2-3x
f(g(x)) = f(2-3x)
f(2-3x) = (2-3x-2)/3
f(2-3x) = -3x/3
f(2-3x) = -x
f(g(x)) = -x for the pair of function
For the pair of function f(x) = x/2 - 2 and g(x) = x/2 + 2
f(g(x)) = f(x/2 + 2)
f(x/2 + 2) = f((x+4)/2)
f((x+4)/2) = [(x+4)/2]/2 - 2
f((x+4)/2) = (x+4)/4 - 2
find the LCM
f((x+4)/2) = [(x+4)-8]/4
f((x+4)/2) = (x-4)/4
Hence f(g(x)) for the pair of function is (x-4)/4
