Mathematics, 21.04.2020 04:52 Ilcienne6590

A chemist prepared ten 4.85 g quantities of aniline and purified it to acetanilide using fractional crystallization. The following dry yields were recorded.

3.83 3.82 3.90 3.87 3.92 3.34 3.64 3.99 3.70 3.85

Estimate the mean grams of acetanilide that can be recovered from an initial amount of 4.85 g of aniline. Use a 95% confidence interval. (Round your answers to three decimal places.)

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Answer from: mollykay2001p3qo0j

$3.786-2.262\frac{0.187}{\sqrt{10}}=3.652$

$3.786+2.262\frac{0.187}{\sqrt{10}}=3.920$

So on this case the 95% confidence interval would be given by (3.652;3.920)

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:

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

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=3.786$

The sample deviation calculated s=0.187

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

df=n-1=10-1=9

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: "=-T.INV(0.025,9)".And we see that $t_{\alpha/2}=2.262$

Now we have everything in order to replace into formula (1):

$3.786-2.262\frac{0.187}{\sqrt{10}}=3.652$

$3.786+2.262\frac{0.187}{\sqrt{10}}=3.920$

So on this case the 95% confidence interval would be given by (3.652;3.920)

Answer from: Quest

10 will be the number of adult tickets and 11 will be the number of children tickets. i hope i could ! good luck : )

Answer from: Quest

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9

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