A group of friends go to the haunted museum

A manufacturer reported a sample mean = 22.0 g and a sample standard deviation = 2.5 g based on a sample of 20 of their products

tester [92]

Answer:

$n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5$

So the answer for this case would be n=5 rounded up to the nearest integer

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".

$\bar X=22$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.5 represent the sample standard deviation

n represent the sample size

ME = 2 represent the margin of error accepted

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (2)

And on this case we have that ME =2 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (3)

We can use as estimator for the population deviation the sample deviation $\hat \sigma = s$

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got $z_{\alpha/2}=1.640$ , replacing into formula (3) we got:

$n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5$

So the answer for this case would be n=5 rounded up to the nearest integer

6 0

3 years ago

Plot the numbers -1 1/2 on the number line below.

UkoKoshka [18]

Answer:

____|__♡__|___|_____________

0

where the heart is go left one and a half point

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2 years ago

The graph of h(x) is shown. Graph of h of x that begins in quadrant two and decreases rapidly following the vertical line which

fgiga [73]

Answer:

x-intercept

The point at which the curve crosses the x-axis, so when y = 0.

From inspection of the graph, the curve appears to cross the x-axis when x = -4, so the x-intercept is (-4, 0)

y-intercept

The point at which the curve crosses the y-axis, so when x = 0.

From inspection of the graph, the curve appears to cross the y-axis when y = -1, so the y-intercept is (0, -1)

Asymptote

A line which the curve gets infinitely close to, but never touches.

From inspection of the graph, the curve appears to get infinitely close to but never touches the vertical line at x = -5, so the vertical asymptote is x = -5

(Please note: we cannot be sure that there is a horizontal asymptote at y = -2 without knowing the equation of the graph, or seeing a larger portion of the graph).

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