8. In the nuclear industry, detailed records are kept of the quantity of plutoni

Question

8. In the nuclear industry, detailed records are kept of the quantity of plutonium received, transported, or used. Each shipment of plutonium pellets received is carefully analyzed to check that the purity and hence the total quantity is as the supplier claims. A particular shipment is analyzed with the following results: 99.93, 99.87, 99.91, and 99.86%. The listed purity as received from the supplier is 99.95%. Is the shipment acceptable at the 95% confidence level? The precision of a method is being established, and the following data are obtained: 22.23.22. 18.22.2522.09, and 22.17%. Is 22.09% a valid measurement at the 95% confidence level? 9. A calibration curve for the colorimetric determination of phosphorous in urine is prepared by reacting standard solutions of phosphate with molybdenum(VI) and reducing the phosphomolybdic acid compl produce the characteristic blue color. The measured absorbance A is plotted against the concentration of phosphorous. From the following data, determine the linear least-squares equation and calculate the phosphorous concentration in the urine sample (use a computer and "Excel") 10. ex to ppm P 1.00 2.00 3.00 4.00 Urine sample Absorbance 0.205 0.410 0.615 0.820 0.625 From the data given below, determine the correlation coefficient between the amount of toxin produced by a fungus and the percent of yeast extract in the growth medium (use a computer and "Excel"). 11. Sample % Yeast Extract 1.000 0.200 0.100 0.010 0.001 Toxin, mg 0.487 0.260 0.195 0.007 0.002

Explanation / Answer

Question 8

Answer:

Here, we have to find the 95% confidence interval for a population mean for the given data and then we have to check whether the listed purity as received from the supplier is contains in the given confidence interval or not.

Confidence interval = Xbar ± t*S/sqrt(n)

We are given data as follow:

Purity (%)

99.93

99.87

99.91

99.86

From given data, we have

Sample mean = Xbar = 99.8925

Sample standard deviation = S = 0.033040379

Sample size = n = 4

Degrees of freedom = n – 1 = 4 – 1 = 3

Confidence level = 95%

Critical t-value = 3.1824

(by using t-table or excel)

Confidence interval = 99.8925 ± 3.1824*0.033040379/sqrt(4)

Confidence interval = 99.8925 ± 3.1824* 0.01652019

Confidence interval = 99.8925 ± 0.0526

Lower limit = 99.8925 - 0.0526 = 99.8399

Upper limit = 99.8925 + 0.0526 = 99.9451

Confidence interval = (99.8399, 99.9451)

Listed purity 99.95% is not contains in the above interval, so the shipment is not acceptable at the 95% confidence level.

Question 9

Answer:

Here, we have to find the 95% confidence interval for a population mean for the given data.

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 22.184

S = 0.062289646

n = 5

Confidence level = 95%

df = n – 1 = 5 – 1 = 4

Critical t value = 2.7764

(by using t-table or excel)

Confidence interval = 22.184 ± 2.7764*0.062289646/sqrt(5)

Confidence interval = 22.184 ± 2.7764* 0.027856777

Confidence interval = 22.184 ± 0.0773

Lower limit = 22.184 - 0.0773 = 22.11

Upper limit = 22.184 + 0.0773 = 22.26

Confidence interval = (22.11%, 22.26%)

22.09% not contains in the above interval, so it is not a valid measurement at the 95% confidence level.

Question 10

Here, we have find the linear least square regression line for estimation of the phosphorous in urine based on absorbance.

Required regression model by using excel is given as below:

Regression Statistics

Multiple R

0.842271401

R Square

0.709421112

Adjusted R Square

0.612561483

Standard Error

0.984172897

Observations

5

ANOVA

df

SS

MS

F

Significance F

Regression

1

7.094211124

7.094211124

7.32421875

0.073391869

Residual

3

2.905788876

0.968596292

Total

4

10

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-0.036322361

1.205178272

-0.030138579

0.977849445

-3.871737499

3.799092777

Absorbance

5.675368899

2.097072487

2.706329387

0.073391869

-0.99845169

12.34918949

Required least square equation for phosphorous concentration is given as below:

Phosphorous concentration = -0.036322361 + 5.675368899*Absorbance

Question 11

Here we have to find the correlation coefficient between the amount of toxin produced by a fungus and the percent of years extract in the growth medium.

% yeast extract

Toxin, mg.

1

0.487

2

0.26

1

0.195

0.01

0.007

0.001

0.002

Correlation coefficient = r = 0.654204579

(By using excel)

There is a considerable positive linear association or relationship exists between the amount of toxin produced by a fungus and the percent of years extract in the growth medium.

Purity (%)

99.93

99.87

99.91

99.86

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