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
Answer:
The opposite of 14 is -14.
Step-by-step explanation:
Opposites are numbers with the same distance from 0 but one is to the right of 0 and the other is to the left of 0.
The opposite of 0 is itself,0.
So the opposite of 5 is -5 since both 5 and -5 have the same distance from 0 and one is to the left and one is to the right of 0.
The opposite of 14 is -14 since both have the same distance from 0 and one is to the right and one is to the left of 0.
You can also think of this question as what can I add to 14 that will give me 0.
The answer is -14 since -14+14=0.
Another word for opposites is additive inverses. When you add additive inverses you get 0.
Another example: What is the opposite of -16?
The answer is 16 since 16+(-16)=0.
hi <3
lets call the unknown number 'x' for now and form an equation from what we know
1/3(x-9) = 15
now multiply both sides by 3
x - 9 = 45
add 9 to both sides
x = 54
hope this helps :)
Answer:
30
Step-by-step explanation:
I think that's the answer but if I'm wrong tell me right away I'll try another method.
Answer:
Step-by-step explanation:Did that help?
