STATISTICS

 Let X  = (X1,...,Xn) be the dignity urgency (measured in mmHg) and let Y = (Y1,...,Yn) be the cortisol flatten (measured in mcg/dL) narrative for n = 79 endurings recruited for a examine in a hospital (Xi and Yi are measurements for the selfselfidentical enduring). What exemplar is most divert to subjoin attraction towards the opinion supposition that dignity urgency is associated followingcited a while cortisol flatten? Please furnish the forced in component for your rejoinder.

A)  The two-exemplification paired t-exemplar followingcited a while the trifling supposition that the media of X and Y be-unlike.

B)  The exemplar followingcited a while the trifling supposition that the Pearson apposition coefficient incomplete X and Y is cipher.

C)  The exemplar followingcited a while the trifling supposition that the retrogression coefficient is cipher in a rectirectirectidirect retrogression followingcited a while vindication inconstant X (dignity urgency) and explanatory inconstant Y (cortisol flatten).

(5 points)

ii)  Suppose that a texture is contemplated to narrow the continuance from the interval of taint era, to the interval at which a chief disclaiming exemplar is narrative in nation followingcited a while lenient COVID-19 (wheedle this interval determination the continuance). Suppose that 27 nation followingcited a while lenient COVID-19 (the examine population) are administered the texture and 73 nation followingcited a while lenient COVID-19 are not administered the

texture (the administer population). Twain populations are exemplificationd from endurings exemplared at the selfselfidentical clinic aggravate the selfselfidentical determination. Let the continuances for the examine exemplification be X = (X1, X2,...), and the continuances for the administer exemplification be Y = (Y1, Y2,...). What exemplar is most divert to subjoin attraction towards the opinion supposition that the texture narrows the continuance? Please furnish the forced for your rejoinder. Please furnish the forced in component for your rejoinder.

A)  The one-sided two-exemplification unpaired t-exemplar followingcited a while H0: The balance of X is greater than or resembling to the balance of Y.

B)  The one-sided two-exemplification unpaired t-exemplar followingcited a while the trifling supposition that the balance of X is less than or resembling to the balance of Y.

C)  The exemplar despite the trifling supposition that the Spearman’s ranked apposition coefficient incomplete X and Y is cipher.

D)  The one-sided two-exemplification paired t-exemplar despite H0: The balance be-unlikeence incomplete Xi and Yi is less than or resembling to cipher.

E)  The two-sided two-exemplification paired t-exemplar followingcited a while the trifling supposition that the balance be-unlikeence incomplete Xi and Yi is zero.

(5 points)

iii)  Road transportation accidents involving ambulances accept balance injurious outcomes than accidents involving other similarly sized transportations (Ray and Kupas, 2005). Measures to quit such accidents are persistently nature genteel by constructions confused in strait medical services. Suppose that a city congress is assiduous in acute if segregation of such measures has bring to an correction aggravate the definite decade. Suppose that the kindred incomplete the compute of accidents 

iv)  involving ambulances (the numerator) and the compute of kilometers driven by ambulances (the denominator) has been narrative (rt followingcited a while units’ compute of accidents per kilometer year) for each year t aggravate the spent decade. Which sepaadmonish one of the followingcitedcited statistical quantities is most relevant 

for investigating whether or not measures are bringing to corrections? Please furnish the forced in component for your rejoinder.

A)  The exemplification exemplar gap of rt.

B)  The exemplification balance of rt.

C)  The Pearson apposition coefficient ρ incomplete rt and t.

D)  The retrogression coefficient for t in a rectirectirectidirect retrogression followingcited a while rt as the vindication inconstant and t as the explanatory inconstant.

E)  The retrogression coefficient for rt in a rectirectirectidirect retrogression followingcited a while rt as the explanatory inconstant and t as the vindication inconstant.

Problem 2: Bayes’ rule

A examine was conducted to assess the sensitivity and specificity of foul-mouthed be-unlikeent ethnical immunodeficiency bane (HIV) serology exemplars (Koblavi-D`eme et al. 2001). The Determine exemplar was incomplete the foul-mouthed, it was open by Abbott Laboratories (an American furnishr of vigor thrift, medical devices and pharmaceuticals) and was ground to accept a gentleman disclaiming admonish (the gentleman disclaiming admonish is too wheedleed specificity) of 99.4% and a gentleman actual admonish (the gentleman actual admonish is too wheedleed sensitivity) of 100%. The gentleman disclaiming admonish of a exemplar for a ailment is the verisimilitude that someone followingcited a whileout the ailment exemplars disclaiming. The gentleman actual admonish of a exemplar for a ailment is the verisimilitude that someone followingcited a while the ailment exemplars actual. HIV may be catching from an expecting cause to their slip by transmission during slipnobility or by transmission to the fetus during pregnancy (throughout, affect that there’s no other way for a newborn to be profligate). Texture by the drugs zidovudine or nevirapine has been shown to narrow the admonish of these sorts of transmission of HIV by 38% to 50% in the neglect of other mediation (Koblavi-D`eme et al. 2001).

a) Suppose that an expecting cause is profligate followingcited a while HIV and they are treated followingcited a while zidovudine or nevirapine during pregnancy. Suppose that followingcited they bestow nobility, a Determine serology exemplar reports a actual exemplar for HIV. What is the verisimilitude that the slip does not accept HIV? Round your rejoinder to the unswerving 10-th of a percent.

 (6 points) 

b) UNAIDS (an construction recurrent by the United Nations Economic and Social Council) estimates the efficacy of HIV in Cˆote d’Ivoire incomplete nation old 15-49 to be 2.6%. If a Determine serology exemplar reported a actual exemplar for HIV in someone separated once at vague incomplete all nation in Cˆote d’Ivoire old 15-49, what is the verisimilitude that the peculiar does not accept HIV? Round your rejoinder to the unswerving 10-th of a percent.

(4 points)

c) In the USA, according to the Centers for Ailment Administer (a general vigor instal followingcited a whilein the United States Department of Vigor and Ethnical Services), if someone has a actual serology exemplar for HIV they are not diagnosed as HIV-actual until a succor follow-up exemplar too yields a actual exemplar consequence. What is the verisimilitude that someone is improperly diagnosed as HIV-actual (i.e., if someone is not profligate followingcited a while HIV, what is the verisimilitude that their chief exemplar and too their succor follow-up exemplar are twain actual)? Suppose that twain exemplars are Determine serology exemplars, and too affect that the exemplar consequences are statistically rebellious. Express your rejoinder in expected compute of events in a pet (i.e. star enjoy ‘a 36 in a pet chance’ or ‘a one in a pet chance’). Also: In one phrase, what is a possible topic as to why the selfreliance of anarchy of the two exemplar consequences influence be evil-doing? (Your topic does not accept to be investigate, but it must be powerful followingcited a whileout nature tautological).

 (3 points) 

d) What is the verisimilitude that an HIV profligate expecting cause transmits HIV to their slip either during slipnobility or through transmitting HIV to the fetus during pregnancy, bestown that the cause has not common texture followingcited a while the drugs zidovudine or nevirapine, and in the neglect of other mediation, according to the opening of this substance (in concordance followingcited a while Koblavi-D`eme et al. 2001)?

(2 points) Let X  = (X1,...,Xn) be the dignity urgency (measured in mmHg) and let Y = (Y1,...,Yn) be the cortisol flatten (measured in mcg/dL) narrative for n = 79 endurings recruited for a examine in a hospital (Xi and Yi are measurements for the selfselfidentical enduring). What exemplar is most divert to subjoin attraction towards the opinion supposition that dignity urgency is associated followingcited a while cortisol flatten? Please furnish the forced in component for your rejoinder.

A)  The two-exemplification paired t-exemplar followingcited a while the trifling supposition that the media of X and Y be-unlike.

B)  The exemplar followingcited a while the trifling supposition that the Pearson apposition coefficient incomplete X and Y is cipher.

C)  The exemplar followingcited a while the trifling supposition that the retrogression coefficient is cipher in a rectirectirectidirect retrogression followingcited a while vindication inconstant X (dignity urgency) and explanatory inconstant Y (cortisol flatten).

(5 points)

ii)  Suppose that a texture is contemplated to narrow the continuance from the interval of taint era, to the interval at which a chief disclaiming exemplar is narrative in nation followingcited a while lenient COVID-19 (wheedle this interval determination the continuance). Suppose that 27 nation followingcited a while lenient COVID-19 (the examine population) are administered the texture and 73 nation followingcited a while lenient COVID-19 are not administered the

texture (the administer population). Twain populations are exemplificationd from endurings exemplared at the selfselfidentical clinic aggravate the selfselfidentical determination. Let the continuances for the examine exemplification be X = (X1, X2,...), and the continuances for the administer exemplification be Y = (Y1, Y2,...). What exemplar is most divert to subjoin attraction towards the opinion supposition that the texture narrows the continuance? Please furnish the forced for your rejoinder. Please furnish the forced in component for your rejoinder.

A)  The one-sided two-exemplification unpaired t-exemplar followingcited a while H0: The balance of X is greater than or resembling to the balance of Y.

B)  The one-sided two-exemplification unpaired t-exemplar followingcited a while the trifling supposition that the balance of X is less than or resembling to the balance of Y.

C)  The exemplar despite the trifling supposition that the Spearman’s ranked apposition coefficient incomplete X and Y is cipher.

D)  The one-sided two-exemplification paired t-exemplar despite H0: The balance be-unlikeence incomplete Xi and Yi is less than or resembling to cipher.

E)  The two-sided two-exemplification paired t-exemplar followingcited a while the trifling supposition that the balance be-unlikeence incomplete Xi and Yi is zero.

(5 points)

iii)  Road transportation accidents involving ambulances accept balance injurious outcomes than accidents involving other similarly sized transportations (Ray and Kupas, 2005). Measures to quit such accidents are persistently nature genteel by constructions confused in strait medical services. Suppose that a city congress is assiduous in acute if segregation of such measures has bring to an correction aggravate the definite decade. Suppose that the kindred incomplete the compute of accidents 

iv)  involving ambulances (the numerator) and the compute of kilometers driven by ambulances (the denominator) has been narrative (rt followingcited a while units’ compute of accidents per kilometer year) for each year t aggravate the spent decade. Which sepaadmonish one of the followingcitedcited statistical quantities is most relevant 

for investigating whether or not measures are bringing to corrections? Please furnish the forced in component for your rejoinder.

A)  The exemplification exemplar gap of rt.

B)  The exemplification balance of rt.

C)  The Pearson apposition coefficient ρ incomplete rt and t.

D)  The retrogression coefficient for t in a rectirectirectidirect retrogression followingcited a while rt as the vindication inconstant and t as the explanatory inconstant.

E)  The retrogression coefficient for rt in a rectirectirectidirect retrogression followingcited a while rt as the explanatory inconstant and t as the vindication inconstant.

Problem 2: Bayes’ rule

A examine was conducted to assess the sensitivity and specificity of foul-mouthed be-unlikeent ethnical immunodeficiency bane (HIV) serology exemplars (Koblavi-D`eme et al. 2001). The Determine exemplar was incomplete the foul-mouthed, it was open by Abbott Laboratories (an American furnishr of vigor thrift, medical devices and pharmaceuticals) and was ground to accept a gentleman disclaiming admonish (the gentleman disclaiming admonish is too wheedleed specificity) of 99.4% and a gentleman actual admonish (the gentleman actual admonish is too wheedleed sensitivity) of 100%. The gentleman disclaiming admonish of a exemplar for a ailment is the verisimilitude that someone followingcited a whileout the ailment exemplars disclaiming. The gentleman actual admonish of a exemplar for a ailment is the verisimilitude that someone followingcited a while the ailment exemplars actual. HIV may be catching from an expecting cause to their slip by transmission during slipnobility or by transmission to the fetus during pregnancy (throughout, affect that there’s no other way for a newborn to be profligate). Texture by the drugs zidovudine or nevirapine has been shown to narrow the admonish of these sorts of transmission of HIV by 38% to 50% in the neglect of other mediation (Koblavi-D`eme et al. 2001).

a) Suppose that an expecting cause is profligate followingcited a while HIV and they are treated followingcited a while zidovudine or nevirapine during pregnancy. Suppose that followingcited they bestow nobility, a Determine serology exemplar reports a actual exemplar for HIV. What is the verisimilitude that the slip does not accept HIV? Round your rejoinder to the unswerving 10-th of a percent.

 (6 points) 

b) UNAIDS (an construction recurrent by the United Nations Economic and Social Council) estimates the efficacy of HIV in Cˆote d’Ivoire incomplete nation old 15-49 to be 2.6%. If a Determine serology exemplar reported a actual exemplar for HIV in someone separated once at vague incomplete all nation in Cˆote d’Ivoire old 15-49, what is the verisimilitude that the peculiar does not accept HIV? Round your rejoinder to the unswerving 10-th of a percent.

(4 points)

c) In the USA, according to the Centers for Ailment Administer (a general vigor instal followingcited a whilein the United States Department of Vigor and Ethnical Services), if someone has a actual serology exemplar for HIV they are not diagnosed as HIV-actual until a succor follow-up exemplar too yields a actual exemplar consequence. What is the verisimilitude that someone is improperly diagnosed as HIV-actual (i.e., if someone is not profligate followingcited a while HIV, what is the verisimilitude that their chief exemplar and too their succor follow-up exemplar are twain actual)? Suppose that twain exemplars are Determine serology exemplars, and too affect that the exemplar consequences are statistically rebellious. Express your rejoinder in expected compute of events in a pet (i.e. star enjoy ‘a 36 in a pet chance’ or ‘a one in a pet chance’). Also: In one phrase, what is a possible topic as to why the selfreliance of anarchy of the two exemplar consequences influence be evil-doing? (Your topic does not accept to be investigate, but it must be powerful followingcited a whileout nature tautological).

 (3 points) 

d) What is the verisimilitude that an HIV profligate expecting cause transmits HIV to their slip either during slipnobility or through transmitting HIV to the fetus during pregnancy, bestown that the cause has not common texture followingcited a while the drugs zidovudine or nevirapine, and in the neglect of other mediation, according to the opening of this substance (in concordance followingcited a while Koblavi-D`eme et al. 2001)?

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