Mathematics, 25.07.2019 06:30 aliyahmuhammad5197

He amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5 construct a 98% confidence interval for the mean amount of juice in all such bottles. assume an approximate normal distribution.

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Answer from: Dolphin56

$15.46-2.998\frac{0.307}{\sqrt{8}}=15.13$

$15.46+2.998\frac{0.307}{\sqrt{8}}=15.79$

So on this case the 98% confidence interval would be given by (15.13;15.79)

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 $\bar X=15.46$

The sample deviation calculated s=0.307

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

df=n-1=8-1=7

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.01,7)".And we see that $t_{\alpha/2}=2.998$

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

$15.46-2.998\frac{0.307}{\sqrt{8}}=15.13$

$15.46+2.998\frac{0.307}{\sqrt{8}}=15.79$

So on this case the 98% confidence interval would be given by (15.13;15.79)

Answer from: Quest

I’m not sure what it is i sorry : ((

Answer from: Quest

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

$\frac{sb}{cs}$ = $\frac{ra}{cr}$ ← substitute values

$\frac{4x+1}{2x}$ = $\frac{13.5}{6}$ ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

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