# Statistics Assignment

Let X  = (X1,...,Xn) be the class urgency (measured in mmHg) and let Y = (Y1,...,Yn) be the cortisol smooth (measured in mcg/dL) chronicled for n = 79 unrepinings recruited for a con-balance in a hospital (Xi and Yi are measurements for the corresponding unrepining). What cupel is most misspend to subjoin manifestation towards the opinion fancy that class urgency is associated forthcoming a while cortisol smooth? Please yield the associationnalistic in particular for your counterpart.

A)  The two-illustration paired t-cupel forthcoming a while the void fancy that the resources of X and Y differ.

B)  The cupel forthcoming a while the void fancy that the Pearson interdependence coefficient betwixt X and Y is naught.

C)  The cupel forthcoming a while the void fancy that the return coefficient is naught in a rectirectirectirectidirect return forthcoming a while tally changeable X (class urgency) and explanatory changeable Y (cortisol smooth).

(5 points)

ii)  Suppose that a tenor is designed to weaken the prolongation from the span of taint space, to the span at which a foremost denying cupel is chronicled in community forthcoming a while modereprove COVID-19 (seduce this span epoch the prolongation). Suppose that 27 community forthcoming a while modereprove COVID-19 (the con-balance population) are administered the tenor and 73 community forthcoming a while modereprove COVID-19 are not administered the

tenor (the govern population). Twain populations are illustrationd from unrepinings cupeled at the corresponding clinic balance the corresponding epoch. Let the prolongations for the con-balance illustration be X = (X1, X2,...), and the prolongations for the govern illustration be Y = (Y1, Y2,...). What cupel is most misspend to subjoin manifestation towards the opinion fancy that the tenor weakens the prolongation? Please yield the associationnalistic for your counterpart. Please yield the associationnalistic in particular for your counterpart.

A)  The one-sided two-sample unpaired t-cupel forthcoming a while H0: The average of X is greater than or correspondent to the average of Y.

B)  The one-sided two-sample unpaired t-cupel forthcoming a while the void fancy that the average of X is less than or correspondent to the average of Y.

C)  The cupel abutting the void fancy that the Spearman’s ranked interdependence coefficient betwixt X and Y is naught.

D)  The one-sided two-sample paired t-cupel abutting H0: The average estrangement betwixt Xi and Yi is less than or correspondent to naught.

E)  The two-sided two-sample paired t-cupel forthcoming a while the void fancy that the average estrangement betwixt Xi and Yi is zero.

(5 points)

iii)  Road behavior accidents involving ambulances keep gone-by hurtful outcomes than accidents involving other similarly sized behaviors (Ray and Kupas, 2005). Measures to eschew such accidents are persistently nature genteel by structures implicated in necessity medical services. Suppose that a city parliament is warinessful in skillful if preoption of such measures has bring to an amendment balance the plain decade. Suppose that the association betwixt the calculate of accidents

iv)  involving ambulances (the numerator) and the calculate of kilometers driven by ambulances (the denominator) has been chronicled (rt forthcoming a while units’ calculate of accidents per kilometer year) for each year t balance the gone-by decade. Which unmarried one of the forthcoming statistical quantities is most relevant

for investigating whether or not measures are bringing to amendments? Please yield the associationnalistic in particular for your counterpart.

A)  The illustration flag sinuosity of rt.

B)  The illustration average of rt.

C)  The Pearson interdependence coefficient ρ between rt and t.

D)  The return coefficient for t in a rectirectirectirectidirect return forthcoming a while rt as the tally changeable and t as the explanatory changeable.

E)  The return coefficient for rt in a rectirectirectirectidirect return forthcoming a while rt as the explanatory changeable and t as the tally changeable.

## Problem 2: Bayes’ rule

A con-balance was conducted to assess the sensitivity and specificity of impure opposed anthropological immunodeficiency bane (HIV) serology cupels (Koblavi-D`eme et al. 2001). The Determine cupel was discurrent the impure, it was plain by Abbott Laboratories (an American yieldr of probeness wariness, medical devices and pharmaceuticals) and was base to keep a gentleman denying reprove (the gentleman denying reprove is besides seduceed specificity) of 99.4% and a gentleman settled reprove (the gentleman settled reprove is besides seduceed sensitivity) of 100%. The gentleman denying reprove of a cupel for a sickness is the appearance that someone forthcoming a whileout the sickness cupels denying. The gentleman settled reprove of a cupel for a sickness is the appearance that someone forthcoming a while the sickness cupels settled. HIV may be epidemic from an expecting cause to their cadet by transmission during cadetorigin or by transmission to the fetus during pregnancy (throughout, usurp that there’s no other way for a newborn to be decayed). Tenor by the drugs zidovudine or nevirapine has been shown to weaken the reprove of these sorts of transmission of HIV by 38% to 50% in the omission of other intercession (Koblavi-D`eme et al. 2001).

a) Suppose that an expecting cause is decayed forthcoming a while HIV and they are treated forthcoming a while zidovudine or nevirapine during pregnancy. Suppose that forthcoming they communicate origin, a Determine serology cupel reports a settled cupel for HIV. What is the appearance that the cadet does not keep HIV? Round your counterpart to the rectidirect 10-th of a percent.

(6 points)

b) UNAIDS (an structure ordinary by the United Nations Economic and Social Council) estimates the influence of HIV in Cˆote d’Ivoire discurrent community old 15-49 to be 2.6%. If a Determine serology cupel reputed a settled cupel for HIV in someone separated unintermittently at wild discurrent all community in Cˆote d’Ivoire old 15-49, what is the appearance that the special does not keep HIV? Round your counterpart to the rectidirect 10-th of a percent.

(4 points)

c) In the USA, according to the Centers for Sickness Govern (a open probeness form forthcoming a whilein the United States Department of Soundness and Anthropological Services), if someone has a settled serology cupel for HIV they are not diagnosed as HIV-settled until a desert follow-up cupel besides yields a settled cupel conclusion. What is the appearance that someone is awry diagnosed as HIV-settled (i.e., if someone is not decayed forthcoming a while HIV, what is the appearance that their foremost cupel and besides their desert follow-up cupel are twain settled)? Suppose that twain cupels are Determine serology cupels, and besides usurp that the cupel conclusions are statistically recalcitrant. Express your counterpart in expected calculate of events in a favorite (i.e. something affect ‘a 36 in a favorite chance’ or ‘a one in a favorite chance’). Also: In one decree, what is a possible rationalistic as to why the selfreliance of anarchy of the two cupel conclusions faculty be evil-doing? (Your harmonynalistic does not keep to be probe, but it must be operative forthcoming a whileout nature tautological).

(3 points)

d) What is the appearance that an HIV decayed expecting cause transmits HIV to their cadet either during cadetorigin or through transmitting HIV to the fetus during pregnancy, communicaten that the cause has not received tenor forthcoming a while the drugs zidovudine or nevirapine, and in the omission of other intercession, according to the introductory of this amount (in concordance forthcoming a while Koblavi-D`eme et al. 2001)?

(2 points) Let X  = (X1,...,Xn) be the class urgency (measured in mmHg) and let Y = (Y1,...,Yn) be the cortisol smooth (measured in mcg/dL) chronicled for n = 79 unrepinings recruited for a con-balance in a hospital (Xi and Yi are measurements for the corresponding unrepining). What cupel is most misspend to subjoin manifestation towards the opinion fancy that class urgency is associated forthcoming a while cortisol smooth? Please yield the associationnalistic in particular for your counterpart.

A)  The two-illustration paired t-cupel forthcoming a while the void fancy that the resources of X and Y differ.

B)  The cupel forthcoming a while the void fancy that the Pearson interdependence coefficient betwixt X and Y is naught.

C)  The cupel forthcoming a while the void fancy that the return coefficient is naught in a rectirectirectirectidirect return forthcoming a while tally changeable X (class urgency) and explanatory changeable Y (cortisol smooth).

(5 points)

ii)  Suppose that a tenor is designed to weaken the prolongation from the span of taint space, to the span at which a foremost denying cupel is chronicled in community forthcoming a while modereprove COVID-19 (seduce this span epoch the prolongation). Suppose that 27 community forthcoming a while modereprove COVID-19 (the con-balance population) are administered the tenor and 73 community forthcoming a while modereprove COVID-19 are not administered the

tenor (the govern population). Twain populations are illustrationd from unrepinings cupeled at the corresponding clinic balance the corresponding epoch. Let the prolongations for the con-balance illustration be X = (X1, X2,...), and the prolongations for the govern illustration be Y = (Y1, Y2,...). What cupel is most misspend to subjoin manifestation towards the opinion fancy that the tenor weakens the prolongation? Please yield the associationnalistic for your counterpart. Please yield the associationnalistic in particular for your counterpart.

A)  The one-sided two-sample unpaired t-cupel forthcoming a while H0: The average of X is greater than or correspondent to the average of Y.

B)  The one-sided two-sample unpaired t-cupel forthcoming a while the void fancy that the average of X is less than or correspondent to the average of Y.

C)  The cupel abutting the void fancy that the Spearman’s ranked interdependence coefficient betwixt X and Y is naught.

D)  The one-sided two-sample paired t-cupel abutting H0: The average estrangement betwixt Xi and Yi is less than or correspondent to naught.

E)  The two-sided two-sample paired t-cupel forthcoming a while the void fancy that the average estrangement betwixt Xi and Yi is zero.

(5 points)

iii)  Road behavior accidents involving ambulances keep gone-by hurtful outcomes than accidents involving other similarly sized behaviors (Ray and Kupas, 2005). Measures to eschew such accidents are persistently nature genteel by structures implicated in necessity medical services. Suppose that a city parliament is warinessful in skillful if preoption of such measures has bring to an amendment balance the plain decade. Suppose that the association betwixt the calculate of accidents

iv)  involving ambulances (the numerator) and the calculate of kilometers driven by ambulances (the denominator) has been chronicled (rt forthcoming a while units’ calculate of accidents per kilometer year) for each year t balance the gone-by decade. Which unmarried one of the forthcoming statistical quantities is most relevant

for investigating whether or not measures are bringing to amendments? Please yield the associationnalistic in particular for your counterpart.

A)  The illustration flag sinuosity of rt.

B)  The illustration average of rt.

C)  The Pearson interdependence coefficient ρ between rt and t.

D)  The return coefficient for t in a rectirectirectirectidirect return forthcoming a while rt as the tally changeable and t as the explanatory changeable.

E)  The return coefficient for rt in a rectirectirectirectidirect return forthcoming a while rt as the explanatory changeable and t as the tally changeable.

## Problem 2: Bayes’ rule

A con-balance was conducted to assess the sensitivity and specificity of impure opposed anthropological immunodeficiency bane (HIV) serology cupels (Koblavi-D`eme et al. 2001). The Determine cupel was discurrent the impure, it was plain by Abbott Laboratories (an American yieldr of probeness wariness, medical devices and pharmaceuticals) and was base to keep a gentleman denying reprove (the gentleman denying reprove is besides seduceed specificity) of 99.4% and a gentleman settled reprove (the gentleman settled reprove is besides seduceed sensitivity) of 100%. The gentleman denying reprove of a cupel for a sickness is the appearance that someone forthcoming a whileout the sickness cupels denying. The gentleman settled reprove of a cupel for a sickness is the appearance that someone forthcoming a while the sickness cupels settled. HIV may be epidemic from an expecting cause to their cadet by transmission during cadetorigin or by transmission to the fetus during pregnancy (throughout, usurp that there’s no other way for a newborn to be decayed). Tenor by the drugs zidovudine or nevirapine has been shown to weaken the reprove of these sorts of transmission of HIV by 38% to 50% in the omission of other intercession (Koblavi-D`eme et al. 2001).

a) Suppose that an expecting cause is decayed forthcoming a while HIV and they are treated forthcoming a while zidovudine or nevirapine during pregnancy. Suppose that forthcoming they communicate origin, a Determine serology cupel reports a settled cupel for HIV. What is the appearance that the cadet does not keep HIV? Round your counterpart to the rectidirect 10-th of a percent.

(6 points)

b) UNAIDS (an structure ordinary by the United Nations Economic and Social Council) estimates the influence of HIV in Cˆote d’Ivoire discurrent community old 15-49 to be 2.6%. If a Determine serology cupel reputed a settled cupel for HIV in someone separated unintermittently at wild discurrent all community in Cˆote d’Ivoire old 15-49, what is the appearance that the special does not keep HIV? Round your counterpart to the rectidirect 10-th of a percent.

(4 points)

c) In the USA, according to the Centers for Sickness Govern (a open probeness form forthcoming a whilein the United States Department of Soundness and Anthropological Services), if someone has a settled serology cupel for HIV they are not diagnosed as HIV-settled until a desert follow-up cupel besides yields a settled cupel conclusion. What is the appearance that someone is awry diagnosed as HIV-settled (i.e., if someone is not decayed forthcoming a while HIV, what is the appearance that their foremost cupel and besides their desert follow-up cupel are twain settled)? Suppose that twain cupels are Determine serology cupels, and besides usurp that the cupel conclusions are statistically recalcitrant. Express your counterpart in expected calculate of events in a favorite (i.e. something affect ‘a 36 in a favorite chance’ or ‘a one in a favorite chance’). Also: In one decree, what is a possible rationalistic as to why the selfreliance of anarchy of the two cupel conclusions faculty be evil-doing? (Your harmonynalistic does not keep to be probe, but it must be operative forthcoming a whileout nature tautological).

(3 points)

d) What is the appearance that an HIV decayed expecting cause transmits HIV to their cadet either during cadetorigin or through transmitting HIV to the fetus during pregnancy, communicaten that the cause has not received tenor forthcoming a while the drugs zidovudine or nevirapine, and in the omission of other intercession, according to the introductory of this amount (in concordance forthcoming a while Koblavi-D`eme et al. 2001)?

(2 points)

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