Mathematics, 06.06.2020 22:58, golderhadashaowtatz

The National Center for Educational Statistics surveyed 5400 college graduates about the lengths of time required to earn their bachelors degrees. The mean is 5.4 years and the standard deviation is 1.9 years. Based on this sample, construct a 90% confidence interval for the mean time required by all college graduates

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answered: lexipooh5954

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

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:

$\alpha = \frac{1-0.9}{2} = 0.05$

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 1-0.05 = 0.95 , so z = 1.645

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.

$M = 1.645*\frac{1.9}{\sqrt{4500}} = 0.04$

The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.

The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

answered: Guest

The answer is the numbers between =5 and 5

answered: Guest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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The National Center for Educational Statistics surveyed 5400 college graduates about the lengths of...