Mathematics, 24.12.2019 18:31 cashhd1212

(co6) in a sample of 15 stuffed animals, you find that they weigh an average of 8.56 ounces with a standard deviation of 0.09 ounces. find the 92% confidence interval.

(8.526, 8.594)
(8.528, 8.591)
(8.510, 8.610)
(8.516, 8.604)

Answers: 3

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Answer from: cuppykittyy

(8.510, 8.610)

Step-by-step explanation:

1) 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".

$\bar X=8.56$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.09 represent the sample standard deviation

n=15 represent the sample size

2) Confidence interval

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

df=n-1=15-1=14

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 table to find the critical value. The excel command would be: "=-T.INV(0.01,14)".And we see that $t_{\alpha/2}=2.62449$

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

$8.56-2.62449\frac{0.09}{\sqrt{15}}=8.500$

$8.56-2.62449\frac{0.09}{\sqrt{15}}=8.621$

So on this case the 95% confidence interval would be given by (8.500;8.621)

If we assume that the population deviation $\sigma=0.09$ then the confidence interval is given by:

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

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 table to find the critical value. The excel command would be: "=-NORM.INV(0.01,1,0)".And we see that $z_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (2):

$8.56-2.33\frac{0.09}{\sqrt{15}}=8.510$

$8.56-2.33\frac{0.09}{\sqrt{15}}=8.614$

So on this case the 95% confidence interval would be given by (8.510;8.610)

Based on this the most accurate answer would be:

(8.510, 8.610)

Answer from: Quest

whatever you can spend with $11.53 or under.

step-by-step explanation:

20 - 8.47 = 11.53. take away the money he used for lunch from the starting amount of 20.

Answer from: Quest

⊂⊃⊂⊃ω $\frac{x}{y}\left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right] \left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right] \\ x^{2} \pi \pi \left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right] \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx x_{123} \left \{ {{y=2} \atop {x=2}} \right. \sqrt[n]{x} x_{123}$

step-by-step explanation:

i hope this : )

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(co6) in a sample of 15 stuffed animals, you find that they weigh an average of 8.56 ounces with a s...