Mathematics, 13.12.2019 03:31 brasherfamily14

For a random sample of 50 measurements on the breaking strength of cotton threads, the mean breaking strength was found to be 210 grams and the standard deviation 18 grams. obtain a confidence interval for the true mean breaking strength of cotton threads of this type, with confidence coefficient 0.99.

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Answer from: isa5166

The 99% confidence interval is given by (203.178;216.822)

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".

$\bar X=210$ represent the sample mean

$\mu$ population mean (variable of interest)

s=18 represent the sample standard deviation

n=50 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=50-1=49

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,49)".And we see that $t_{\alpha/2}=2.68$

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

$210-2.68\frac{18}{\sqrt{50}}=203.178$

$210+2.68\frac{18}{\sqrt{50}}=216.822$

So on this case the 99% confidence interval would be given by (203.178;216.822)

Answer from: Quest

deez nu tz

step-by-step explanation:

Answer from: Quest

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.

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