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ZanzabumX [31]
3 years ago
13

It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to est

imate the GPA within at the confidence level? The population standard deviation is . If needed, round your final answer up to the next whole number.
Mathematics
1 answer:
kenny6666 [7]3 years ago
7 0

Answer:

n=(\frac{2.58(1.2)}{0.25})^2 =153.36 \approx 154

So the answer for this case would be n=154 rounded up to the nearest integer

Step-by-step explanation:

Assuming the following question: It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.25 at the 99% confidence level? The population standard deviation is 1.2. If needed, round your final answer up to the next whole number.

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 represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

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

And on this case we have that ME =0.25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got z_{\alpha/2}=2.58, replacing into formula (b) we got:

n=(\frac{2.58(1.2)}{0.25})^2 =153.36 \approx 154

So the answer for this case would be n=154 rounded up to the nearest integer

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Reptile [31]

Answer:

13/14 is greater

Step-by-step explanation:

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10 x 7        70

<u>13 x 5 </u>    = <u>65</u>

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5 0
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MrRa [10]

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Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Since 2 and -2 are neither of these, your answer is neither.

7 0
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An insurance company has written 52 policies of $50,000, 477 of $25,000, and 918 of $10,000
Ede4ka [16]

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<h3>How to find the expected Value?</h3>

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ella [17]
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5 0
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PolarNik [594]

Answer:

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Step-by-step explanation:

x^2(y+z)+y(y+z)

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basically you distrinbute the first bracket to the second bracket

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