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storchak [24]
3 years ago
5

A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean, what nu

mber of degrees of freedom should be used to determine the appropriate t-value?
Mathematics
1 answer:
kumpel [21]3 years ago
8 0

Answer:

For this case since the sample size is lower than 30 , n =20<30, is not appropiate use the normal standard distribution to calculate the confidence interval for the mean, and then for this case is better use the t distribution since takes in count the correction factor to approximate the distribution of the true parameter.

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

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

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 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

For this case since the sample size is lower than 30 , n =20<30, is not appropiate use the normal standard distribution to calculate the confidence interval for the mean, and then for this case is better use the t distribution since takes in count the correction factor to approximate the distribution of the true parameter.

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

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

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The larger of two numbers is 5 more than the smaller. The smaller number plus the larger equals 100. Find the number.
I am Lyosha [343]

Answer:

Smaller number-47.5

Larger number-52.5

Step-by-step explanation:

We will make the smaller number x. If the smaller number is x, then the larger number will be equal to x+5. We also know that when we add the two numbers, we get 100. We can make the equation

x+x+5=100

100-5=95

2x=95

95/2=47.5

x=47.5

The smaller number equals 47.5 and the larger number is 47.5+5 which equals 52.5

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Answer:

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Step-by-step explanation:

To find the slope intercept form, we know the m(slope) but we need to find b.

y and x is given to us, so we can find b.

Plug in the numbers provided into the slope intercept form.

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To find b, we have to get b by itself. So, we subtract both sides by 24.

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Now that we found b, we can plug this into the equation.

y=12x-4

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First, you would subtract 29.95 from 55.50, and you get 25.55. because 5 people went, and the cost for each was the same, you would divide 25.55 by five, and get $5.11 per person.
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Step-by-step explanation:

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