Mathematics, 21.12.2019 00:31 thompsonhomes1

Ascientist measured the speed of light. his values are in km/sec and have 299,000 subtracted from them. he reported the results of 25 trials with a mean of 756.22 and a standard deviation of 100.89.

(a) find a 90% confidence interval for the true speed of light from these statistics.
(b) state in words what this interval means. keep in mind that the speed of light is a physical constant that, as far as we know, has a value that is true throughout the universe.
(c) what assumptions must you make in order to use your method?

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Answer from: wavymoney77yt

a) The 90% confidence interval would be given by (721.716;790.724)

b) We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)

c) We assume the following conditions:

RandomizationIndependenceDeviation unknown $\sigma$

Step-by-step explanation:

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".

Part a

$\bar X=756.22$ represent the sample mean

$\mu$ population mean (variable of interest)

s=100.89 represent the sample standard deviation

n=25 represent the sample size

90% 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)

The degrees of freedom are given by:

df=n-1=25-1=24

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(0.05,24)".And we see that $t_{\alpha/2}=1.71$

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

$756.22-1.71\frac{100.89}{\sqrt{25}}=721.716$

$756.22+1.71\frac{100.89}{\sqrt{25}}=790.724$

So on this case the 90% confidence interval would be given by (721.716;790.724)

Part b

We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)

Part c

We assume the following conditions:

RandomizationIndependenceDeviation unknown $\sigma$

Answer from: Quest

the answer to this question is yes

Answer from: Quest

1200 inches = 30 yards12 inches= 1 foot3 feet= 1 yard3feet= 36 inchesyou can set up a proportion then use inverse operations that looks sorry it looks so sloppy lol

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