Mathematics, 20.04.2020 23:08 ameliaparry123p2eupk

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 0.005 microcurie per milliliter, respectively. Suppose the researchers want to increase the sample size in order to estimate the mean μ to within 0.002 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?
b. What is the sampling error desired by the researchers?
c. Compute the sample size necessary to obtain the desired estimate.

Answers: 3

Show answers

Answers

Answer from: friezaforceelite

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

(b) The sampling error is 0.002 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:

$\bar x=0.009\\s=0.005$

Now it is provided that the researchers want to increase the sample size in order to estimate the mean μ to within 0.002 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 0.002 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.

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

$0.002=1.96\times \frac{0.005}{\sqrt{n}}$

$n=[\frac{1.96\times 0.005}{0.002}]^{2}$

$=(4.9)^{2}\\=24.01\\\approx 25$

Thus, the sample size necessary to obtain the desired estimate is 25.

Answer from: Quest

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation:

Answer from: Quest

Ibelieve the answer would be 7, 13, 23

Another question on Mathematics

Mathematics, 21.06.2019 18:30

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12

Answers: 1

Answer

Mathematics, 21.06.2019 19:10

If $740 is invested at an interest rate of 11% per year and is compounded continuously, how much will the investment be worth in 7 years? use the continuous compound interest formula a = pert.

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

The angles in a triangle are represented by 5x, 8x, and 2x+9. what is the value of ? a.10.8 b.11.4 c.9.7 d.7.2

Answers: 2

Answer

You know the right answer?

In a sample of nequals16 lichen specimens, the researchers found the mean and standard deviation of...

Questions