Mathematics, 05.05.2020 16:09 ballbritez

We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?

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Answer from: garzacon8822

The 95% confidence interval for the population mean is between 25.86 and 28.14

mean (μ) = 27, standard deviation (σ) = 3.5, sample size (n) = 36

Confidence (C) = 95% = 0.95

α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.025

The z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is equal to 1.96.

The margin of error (E) is:

$E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } =1.96*\frac{3.5}{\sqrt{36} } =1.14$

The confidence interval = μ ± E = (27 ± 1.14) = (25.86, 28.14)

The 95% confidence interval for the population mean is between 25.86 and 28.14

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Answer from: avillarreal332

The 95% confidence interval for the population mean is between 25.86 and 28.14.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of 1-0.025 = 0.975 , so z = 1.96

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{3.5}{\sqrt{36}} = 1.14$

The lower end of the interval is the sample mean subtracted by M. So it is 27 - 1.14 = 25.86

The upper end of the interval is the sample mean added to M. So it is 27 + 1.14 = 28.14

The 95% confidence interval for the population mean is between 25.86 and 28.14.

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

Answer from: Quest

These are the multiples of 15 but what you are probably asking or what are the factors of 15

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