1. It is hypothesized that there are fluctuations in norepinephrine (NE) levelswhich accompany fluctuations in affect with bipolar affective disorder(manic-depressive illness). Thus, during depressive states, NE levels drop;during manic states, NE levels increase. To test this relationship,researchers measured the level of NE by measuring the metabolite 3-methoxy-4-hydroxyphenylglycol (MHPG in micro gram per 24 hour) in thepatient's urine experiencing varying levels of mania/depression. Increasedlevels of MHPG are correlated with increased metabolism (thus higherlevels) of central nervous system NE. Levels of mania/depression were alsorecorded on a scale with a low score indicating increased mania and ahigh score increased depression. The data is provided below.MHPG Affect9802212092614038.1950101814 51280191073 271066128802377628Requirements:1. Draw the Scatter Plot2. Compute for the correlation coefficient usinga. Pearson Correlation Coefficient rb. Spearman Rank Correlation CoefficientFor both, interpret the result concerning the relationship betweenMHPG levels and affect?

The scatter plot is used to represent the relation between two variables graphically. If the data…

Answered: 1. It is hypothesized that there are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.
A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…
For some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If m1 is the frequency at age t1, and m2 is the frequency at age t2, then the yearly rate of increase is estimated by r = (m2 − m1)/(t2 − t1). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be 17.7 ± 1.7 per μgDNA, and the frequency in 40-year-old men was estimated to be 35.9 ± 5.8 per μg DNA. Assume that age is measured with negligible uncertainty.a) Estimate the yearly rate of increase, and find the uncertainty in the estimate.b) Find the relative uncertainty in the estimated rate of increase.
A researcher wishes to study the relationship between education and income separately for individuals who have college degrees, and for those who don't. To this end, he interviews 100 individuals in each category. Survey results are listed in the table below. non college graduates college graduates avg education 13 yr 18 yr std. dev. education 2 yr 1.2 yr Sxx 396 yr2 143 yr2 Avg. Income $67,200 $84,950 std. dev. income $9,400 $10,500 correlation coefficient .25 .15 a. Use the data above to find point estimates for regression coefficients B0NG and B1NG for non-college graduates and BoG and B1G for college graduates. b. Propose an unbiased estimator for the difference theta=B1G - B1NG in slope coefficients for the two sub-populations, and show that B(theta hat)= 0. c. Assume that the error terms ENG and EG for non-graduates and graduates, respectively, are both distributed normally, with known standard deviation oENG = oEG = $ 10,000. In that case, determine the…
Consider the following data on 20 chemical reactions, with Y = chromatographic retention time (seconds) and X = molecular weight (gm/mole). Retention Time and Molecular Weight (n = 20) Name RetentionTime Molecular Weight alpha-pinene 234.50 136.24 cyclopentene 95.27 68.12 p-diethyl benzene 284.00 134.22 decane 250.60 142.29 toluene 174.00 92.14 benzene 135.70 78.11 2-methyl pentane 97.24 86.18 2,3 dimethylbutane 100.70 86.18 1,7-octadiene 172.20 110.20 1,2,4-trimethyl benzene 262.70 120.19 2,3,4-trimethyl pentane 160.98 114.23 ethylcyclohexane 195.07 112.22 limonene 271.50 136.24 methyl cyclohexane 153.57 98.19 m-diethyl benzene 281.50 134.22 2,3-dimethyl pentane 131.83 100.20 2,2-dimethyl butane 89.34 86.18 pentane 78.00 72.15 isooctane 136.90 114.23 hexane 106.00 86.18…
A research group is interested in the relationship between exposure to mold in households after a major hurricane and the onset of acute respiratory illness in children. Suppose an observational study is conducted over 10 years following the natural disaster and the following two-by-two table was created in order to address the relationship between exposure and outcome. Acute Respiratory Illness No Acute Respiratory Illness Total Mold 378 156 534 No Mold 73 260 333 Total 451 416 867 Calculate the incidence of acute respiratory illness in the exposed and unexposed. Calculate the relative risk for ARI due to exposure in this study Interpret your findings from part B
QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis?
Question 1) Consider the following context: The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their insensitivity to that food allergen. Preliminary clinical trials yielded that 25% of the volunteers who suspected they had food allergies were clinically identified as sensitive or intolerant to the food allergen; unfortunately and disappointingly, only 10% of those who tested positive in the clinic also tested positive with the kit. Furthermore, of those self-reporting adult volunteers who had a negative clinic outcome, 5% tested positive anyway with the kit. How many complete branches, from start to finish, would a tree diagram that models this context include? H Question 2) The nutrition and food science division of Farnsworth Pharmaceuticals is alpha testing an OTC diagnostic kit so that adults who self-report a certain food allergy can affirm their…
1) The following data show the results of a study based on the number of hours college students spend playing video games and their GPAs: Number of Hours Playing Video Games(per week)= 42 GPA= 0.2Number of Hours Playing Video Games(per week)= 38 GPA= 0.9Number of Hours Playing Video Games(per week) = 32 GPA= 1.0Number of Hours Playing Video Games(per week) = 26 GPA = 1.1Number of Hours Playing Video Games(per week) = 23 GPA= 1.2Number of Hours Playing Video Games(per week) = 19 GPA= 2.5Number of Hours Playing Video Games(per week) = 15 GPA = 3.0 a) Create a scatter plot and be sure to LABEL BOTH axis and give the chart an overall name. Have the graph display the “r-value” and the correct equation.b) What kind of correlation is this?c) Is this more of a linear or exponential model? Why?d) Predict the standard GPA if a student spends one hour a week playing videogames.
In a detailed study of the productivity of a laboratory, the age distribution of its workers was analyzed, and the results were as follows, the kurtosis coefficient is equal to
Recent publications have addressed the growing concern in the scientific community around the increased prevalence of CAT scans in children between the ages of 7-18 and the growing rate of childhood cancers. Suppose the researcher plans to gather a SRS from a group of children in this age range who have received one or more CAT scans, and a SRS from a group of children who have never received a CAT scan and compare the number of cases of childhood cancers that develop over a prolonged period of time. Assume the following table summarizes the descriptive statistics for his samples. Population Average cases of childhood cancers Standard deviaton Sample size >CAT scan 24.6 2.4 1,894 No CAT scans 11.4 1.9 2,745 A) Carry out the appropriate statistical test to answer the researcher’s hypothesis regarding the difference in average cases of childhood cancers in children aged 7-18 receiving one or more CAT scans versus those that have never received a CAT scan. Use an alpha level…

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