HW2 Fall 2023

xlsx

School

Louisiana State University *

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Course

2001

Subject

Statistics

Date

Feb 20, 2024

Type

xlsx

Pages

26

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Homework 2 Post your answers to the Moodle Assignment section. RENAME the file with your own name included in the filename. You must show your own work (charts & formulas) to receive full credit. You may either add new sheets or enter answers on the question sheets. Use the appropriate numbers of significant figures for each question.
Question Your score 1A 4 1B 4 1C 2 2A 5 2B 5 3A 5 3B 5 3C 5 3D 5 4A 10 4B 10 4C 15 5A 5 5B 10 5C 10 total 100 0 possible points
before 1 month later ID mm Hg mm Hg 1 166 102 2 166 110 3 135 95 4 158 98 5 144 110 6 225 210 7 164 109 8 158 98 9 152 108 10 154 106 control (untreated) treated test subjects
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Q-test. (10 points) A researcher conducted a study of a new drug for lowering blood pressure. Blood pressure measurements from 10 patients were obtained before and after one week of medic A.) Is there a statistical difference between the means of the two groups? (t-test) In other words, did the new medication work for lowering patient blood pressure? You must show your work for full credit. (4 pts) B.) Can the values measured for patient #6 be discarded using the Q-test for statistical outliers? (4 C.) Prepare a chart or graph comparing the results. (2 pts) 1 2 3 4 5 6 7 8 9 10 0 50 100 150 200 250 Blood Pressure Study control (untreated) mm Hg treated test subjects mm Hg Subject Identifications Blood Pressure (mmHg)
t-Test: Paired Two Sample for Means P-value 3.44299878662237E-06 Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df Yes t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail There is a statistical significant difference between the means of the two groups. The p-value is 3.44E-06 which is less than 0.05. Less than 0.05 concludes the whether the results is statistically significant.
Variable 1 Variable 2 162.2 114.6 583.7333333 1154.044444 10 10 0.921877751 0 9 10.0463783 1.721499E-06 1.833112933 3.442999E-06 2.262157163
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Grubbs test (10 points) The following set of data shows 8 mass spectrometer measurements on a 199.31 199.53 200.19 200.82 201.92 201.95 202.18 245.57 A.) Using the Grubbs test, is the highest value an outlier at 5% confidenc B.) Using the Grubbs test, is the lowest value an outlier the 5% confidenc Data Set 199.31 Grubb's Test 199.53 A 2.468765 vs 2.03 200.19 Yes, the highest data point is a outlier 200.82 B 0.449375 vs 2.03 201.92 No, the lowest data point is not an outlier 201.95 202.18 245.57 Max 245.57 Min 199.31 Mean 206.43375 StD 15.8525644
uranium isotope. ce level? (5 points) ce level? (5 points)
iron - AAS iron - ICP ID mg/kg mg/kg 1 4.566 4.622 2 1.655 1.799 3 1.256 1.399 4 0.985 0.998 5 0.302 0.395 6 4.322 4.523 7 5.401 5.423 8 3.012 3.211 9 6.332 6.450 10 6.335 6.533 11 6.888 7.123 12 7.245 7.421 13 4.566 4.622 14 1.655 1.799 15 1.256 1.399 16 0.985 0.998 17 0.302 0.395 18 4.322 4.523 19 4.401 4.425 20 3.012 3.065 21 6.332 6.450 22 6.335 6.533 23 6.888 7.123 24 7.245 7.366 25 10.045 10.400 26 10.666 10.800 27 9.882 9.960 28 9.123 9.206 29 9.622 9.598 30 10.998 11.110 31 8.742 8.924 Avg 5.312 5.438 Sdv 3.3042796062 3.323894431 Max 10.998 11.110 Min 0.302 0.395
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F-test for two sample means. (20 points) Ore samples from the lunar surface were brought to a NASA laboratory for metal analysis using bo The measurements for iron content are shown in the table. A. Calculate the F-test statistic for the two data sets in column C and D. (5 pts) B. What is the F-test statistic from the table on page 63 of your text book to be used for compariso C. Is the precision of the two measurements statistically different according to your comparison of D. Prepare a chart or graph comparing the results. (5 pts) 0 5 10 15 20 25 30 35 0 2 4 6 8 10 12 Part D iron - AAS iron - ICP
Avg 5.31 5.44 Sdv 3.30 3.32 Max 11.00 11.11 Min 0.30 0.40 F-Test Two-Sample for Variances Variable 1 Variable 2 Mean 5.312129032 5.438484 Variance 10.91826372 11.04827 Observations 31 31 df 30 30 F 0.988232508 P(F<=f) one-tail 0.487176754 F Critical one-tail 0.543220913
Linear regression. (35 points) Calibration data using atomic absorption spectrophotometry (AAS) is shown i Ground water samples were taken from Baton Rouge, New Orleans and Hamm The values are reported in absorbance units. A.) Prepare a calibration curve for each of the metals. (10 pts) B.) Add a trendline and regression parameters (correlation coefficient and equ note: Some of the calibration points may need to be excluded, select the best f C.) Using the linear regression equation for a straight line (0.995 criteria) calcu Calibration data - AAS 0.00 0.002 0.002 1.00 0.020 0.060 2.00 0.038 0.119 3.00 0.049 0.177 4.00 0.062 0.245 5.00 0.078 0.297 10.0 0.151 0.595 15.0 0.226 0.732 Sample 1 - BTR 0.135 0.036 Sample 2 - NO 0.109 0.012 Sample 3 - Hammond 0.044 0.033 For best fit line: calibration coefficient (R squared): 0.9993 0.9998 0.0147 0.0594 intercept (b): 0.0046 0.0014 linear range: 0-15 0-10 concentration sample 1: 8.87 0.58 concentration (mg/L) Lead (absorbance) copper (absorbance) slope ( m ):
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concentration sample 2: 7.10 0.18 concentration sample 3: 2.68 0.53 y=mx+b y-b=mx x= (y-b)/m 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 f(x) = 0.09309347826087 x + 0.018380434782609 R² = 0.998571235230799 Zinc (absorbance)
in the table for several priority pollutants. mond, and tested for these metals. uation for a straight line) for each of the calibration curves. (10 pts) fit line and indicate the linear range for each metal. ulate the amount of metal in each sample. (15 pts) 0.003 0.006 0.000 0.051 0.102 0.202 0.102 0.206 0.405 0.154 0.307 0.611 0.212 0.401 0.823 0.262 0.498 1.011 0.518 0.936 1.522 0.788 1.222 1.866 0.024 0.058 0.089 0.155 0.063 0.052 0.106 0.099 0.069 0.9999 0.9986 0.9998 0.0524 0.0931 0.2035 0.0006 0.0184 0.0002 0-15 0-10 0-5 0.45 0.43 0.44 Chromium (absorbance) Zinc (absorbance) Mercury (absorbance) 0.00 2.00 4.00 0.000 0.050 0.100 0.150 0.200 0.250 f(x) = 0.014727 R² = 0.9993303 0.600 0.700 f(x) = 0.059419 R² = 0.9997962
2.95 0.48 0.25 2.01 0.87 0.34 0.00 2.00 0.000 0.100 0.200 0.300 0.400 0.500 R² = 0.9997962 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 000 100 200 300 400 500 600 700 800 900 f(x) = 0.052361111111111 x − 0.000555555555556 R² = 0.999858120872012 Chromium (absorbance) 0.00 1.00 2.00 0.000 0.200 0.400 0.600 0.800 1.000 1.200 f(x) = 0.2035428571428 R² = 0.99982117312322 Me (ab
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0 6.00 8.00 10.00 12.00 14.00 16.00 7777777778 x + 0.004611111111111 395548673 Lead (absorbance) 9565217391 x + 0.001358695652174 223504479 copper (absorbance)
4.00 6.00 8.00 10.00 12.00 223504479 3.00 4.00 5.00 6.00 857 x − 0.000190476190476 24 ercury bsorbance)
silver-AAS silver-ICP mg/kg mg/kg 1 4.566 4.655 2 1.655 1.586 3 1.256 1.322 4 0.985 1.102 5 0.302 0.265 6 4.322 4.566 7 5.401 5.233 8 3.012 3.322 9 6.332 6.233 10 6.335 6.335 11 6.888 6.789 12 7.245 7.215 13 4.566 4.655 14 1.655 1.666 15 1.256 1.263 16 0.985 0.992 17 0.302 0.308 18 4.322 4.269 19 5.401 5.396 20 3.012 3.069 21 6.332 6.299 22 6.335 6.255 23 6.888 6.815 24 7.245 7.206 25 10.045 10.023 26 10.666 10.598 27 9.888 9.996 28 9.123 9.122 29 9.622 9.619 30 10.998 11.102 31 8.742 8.698 32 6.665 6.644 33 6.356 6.346 34 7.123 7.098
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35 8.226 8.298 36 4.663 4.645 37 8.075 8.099 38 6.023 6.033 39 8.002 8.064 40 5.663 5.612 41 7.566 7.513 42 9.044 9.032 43 2.223 2.213 44 3.996 3.898 45 10.521 10.532 46 5.023 5.043 47 8.015 8.011 48 3.023 3.045 49 5.122 5.096 50 6.223 6.115 51 4.999 5.006 52 6.066 6.081 53 6.552 6.459 54 2.123 2.106 55 1.113 1.109 56 2.123 2.119 57 3.123 3.119 58 3.888 3.855 59 6.445 6.345 60 2.355 2.411
T-test for two sample means. (25 points) Sixty ore samples from a mine in Colorado were analyzed for silver using both AAS and ICP. The measurements are shown in the table. A. What is the average value, standard deviation, max and min for each set of measurements? Calculate the statistics separately for AAS versus ICP to compare columns B and C. (5 pts) C. Assuming equal variances, are the means the same for both data sets? Apply the t-test and explain your results. (10 pts) B. Plot the data and customize the chart. Bonus points will be given for artistic innovation. (prepare a chart of some type that makes sense, label clearly). (10 pts) The p-value is 0.997 which is greater than 0.05. This concludes that the data between silver-AAS and silv ICP are not significantly different. 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 0.000 5.000 10.000 15.000 20.000 25.000 Silver Samples (AAS and ICP) silver-AAS mg/kg silver-ICP mg/kg
AAS ICP Average 5.43 5.43 StD 2.87 2.86 Max 11.0 11.1 Min 0.302 0.265 t-Test: Two-Sample Assuming Equal Variances Bins 0 Variable 1 Variable 2 1 Mean 5.433683333 5.432017 2 Variance 8.210804491 8.155882 3 Observations 60 60 4 Pooled Variance 8.183343373 5 Hypothesized Mean Difference 0 6 df 118 7 t Stat 0.003191126 8 P(T<=t) one-tail 0.498729621 9 t Critical one-tail 1.657869522 10 P(T<=t) two-tail 0.997459243 11 t Critical two-tail 1.980272249 12
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Bin Frequency 0 0 1 4 2 5 3 4 4 6 5 6 6 5 7 13 8 4 9 5 10 4 11 4 12 0 More 0 0 1 2 3 4 5 6 7 8 9 10 11 12 More 0 2 4 6 8 10 12 14 Histogram - AAS Bin Frequency
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Frequency 0 1 2 3 4 5 6 7 8 9 10 11 12 More 0 2 4 6 8 10 12 14 Histogram - ICP Freq Bin Frequency
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quency
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Bin Frequency 0 0 1 3 2 6 3 4 4 6 5 5 6 6 7 13 8 4 9 5 10 4 11 3 12 1 More 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Mor 0 2 4 6 8 10 12 14 Histogram - ICP Bin Frequency
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re Frequency
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