Mathematics, 13.03.2020 00:12 rtryf57rfgth

Ecn 221 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.0873.1313.2413.2413.2703.3533.400 3.4113.4373.477 Click here for the Excel Data File (a) Construct a 90% confidence interval for the true mean weight. (Round your answers to 4 decimal places.)

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Answer from: xmanavongrove55

$3.3048-1.83\frac{0.132}{\sqrt{10}}=3.2284$

$3.3048 +1.83\frac{0.132}{\sqrt{10}}=3.3812$

So on this case the 90% confidence interval would be given by (3.2284;3.3812)

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

Data: 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

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 $\bar X=3.3048$

The sample deviation calculated s=0.132

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 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,9)".And we see that $t_{\alpha/2}=1.83$

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

$3.3048-1.83\frac{0.132}{\sqrt{10}}=3.2284$

$3.3048 +1.83\frac{0.132}{\sqrt{10}}=3.3812$

So on this case the 90% confidence interval would be given by (3.2284;3.3812)

Answer from: Quest

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

Answer from: Quest

you'll just earn points here

step-by-step explanation:

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