Mathematics, 15.04.2020 17:18 Nonniel0v3

The University College is interested in the average number of hours per week that freshmen spend going to parties. They took a random sample of 300 freshmen and calculated a mean of 6 hours a week going to parties and a 95% confidence interval for the population mean to be 4 to 8 hours a week. Based on this information, what was their standard error of the mean?

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Answer from: lacyfigueroa

And the confidence interval is given by:

$4 \leq \mu \leq 8$

We can estimate the margin of error like this:

$ME = \frac{8-4}{2}= 2$

And the margin of error is given by:

$ME=z_{\alpha/2} SE$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

And solving for the standard error we got:

$SE= \frac{2}{1.96}= 1.02$

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

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

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

And the confidence interval is given by:

$4 \leq \mu \leq 8$

We can estimate the margin of error like this:

$ME = \frac{8-4}{2}= 2$

And the margin of error is given by:

$ME=z_{\alpha/2} SE$

And solving for the standard error we got:

$SE= \frac{2}{1.96}= 1.02$

Answer from: Quest

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

Answer from: Quest

step-by-step explanation:

because 1/3 is a fraction. we can tell because there is a divisor symbol between the 1 and the 3. if we were to add 2 fractions together, we would add the numerators, which is the number on top, but not the denominators, which is the number on the bottom

1/3+1/3=2/3

hope this !

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