Mathematics, 21.04.2020 15:48 iwannasleep

In a sample of nequals16 lichen specimens, the researchers found the mean and standard deviation of the amount of the radioactive element, cesium-137, that was present to be 0.009 and 0.003 microcurie per milliliter, respectively. Suppose the researchers want to increase the sample size in order to estimate the mean mu to within 0.001 microcurie per milliliter of its true value, using a 95% confidence interval. Complete parts a through c. a. What is the confidence level desired by the researchers? The confidence level is 95. b. What is the sampling error desired by the researchers? The sampling error is 0.001. c. Compute the sample size necessary to obtain the desired estimate. The sample size is nothing. (Type a whole number.)

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Answer from: supersquad907p2m3vo

(a) The confidence level desired by the researchers is 95%.

(b) The sampling error is 0.001 microcurie per millilitre.

Step-by-step explanation:

The mean and standard deviation of the amount of the radioactive element, cesium-137 present in a sample of n = 16 lichen specimen are:

$\bar x=0.009\\s=0.003$

Now it is provided that the researchers want to increase the sample size in order to estimate the mean μ to within 0.001 microcurie per millilitre of its true value, using a 95% confidence interval.

The (1 - α)% confidence interval for population mean (μ) is:

$CI=\bar x \pm z_{\alpha/2}\times \frac{s}{\sqrt{n}}$

(a)

The confidence level is the probability that a particular value of the parameter under study falls within a specific interval of values.

In this case the researches wants to estimate the mean using the 95% confidence interval.

Thus, the confidence level desired by the researchers is 95%.

(b)

In case of statistical analysis, during the computation of a certain statistic, to estimate the value of the parameter under study, certain error occurs which are known as the sampling error.

In case of the estimate of parameter using a confidence interval the sampling error is known as the margin of error.

In this case the margin of error is 0.001 microcurie per millilitre.

(c)

The margin of error is computed using the formula:

$MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}$

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size value as follows:

$MOE=z_{\alpha/2}\times \frac{s}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times s}{MOE}]^{2}$

$=[\frac{1.96\times 0.003}{0.001}]^{2}$

$=34.5744\\\approx36$

Thus, the sample size necessary to obtain the desired estimate is 36.

Answer from: Quest

1. 0.3 •4 is the same as 4 groups of 0.32. 7•0.8 is the same as 7 groups of 0.83. it increases by 0.5 every time, so 0.5x4 it increases by 0.9 every time, so 0.9x5. 0.9•12=10.86. 0.47•5=2.35i can finish the next ones in a separate post
Can someone plz me 1 to 37 . i will earn 10 points

Can someone plz me 1 to 37 . i will earn 10 points

Answer from: Quest

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)
I’m not sure how to solve these type of problems

I’m not sure how to solve these type of problems

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