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10.8 Homework  (Page 6/7)

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For questions [link] – [link] , use the following information.

A new AIDS prevention drugs was tried on a group of 224 HIV positive patients. Forty-five (45) patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same.

Let the subscript t size 12{t} {} = treated patient and ut size 12{ ital "ut"} {} = untreated patient.

The appropriate hypotheses are:

  • H o : p t < p ut size 12{H rSub { size 8{o} } :p rSub { size 8{t} }<p rSub { size 8{ ital "ut"} } } {} and H a : p t ≥ p ut size 12{H rSub { size 8{a} } :p rSub { size 8{t} }>= p rSub { size 8{ ital "ut"} } } {}
  • H o : p t ≤ p ut size 12{H rSub { size 8{o} } :p rSub { size 8{t} }<= p rSub { size 8{ ital "ut"} } } {} and H a : p t > p ut size 12{H rSub { size 8{a} } :p rSub { size 8{t} }>p rSub { size 8{ ital "ut"} } } {}
  • H o : p t = p ut size 12{H rSub { size 8{o} } :p rSub { size 8{t} } =p rSub { size 8{ ital "ut"} } } {} and H a : p t ≠ p ut size 12{H rSub { size 8{a} } :p rSub { size 8{t} }<>p rSub { size 8{ ital "ut"} } } {}
  • H o : p t = p ut size 12{H rSub { size 8{o} } :p rSub { size 8{t} } =p rSub { size 8{ ital "ut"} } } {} and H a : p t < p ut size 12{H rSub { size 8{a} } :p rSub { size 8{t} }<p rSub { size 8{ ital "ut"} } } {}

D

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If the p -value is 0.0062 what is the conclusion (use α = 0.05 size 12{α=5%} {} )?

  • The method has no effect.
  • There is sufficient evidence to conclude that the method reduces the proportion of HIV positive patients that develop AIDS after four years.
  • There is sufficient evidence to conclude that the method increases the proportion of HIV positive patients that develop AIDS after four years.
  • There is insufficient evidence to conclude that the method reduces the proportion of HIV positive patients that develop AIDS after four years.

B

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Lesley E. Tan investigated the relationship between left-handedness and right-handedness and motor competence in preschool children. Random samples of 41 left-handers and 41 right-handers were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown below. Determine the appropriate test and best distribution to use for that test.

Left-handed Right-handed
Sample size 41 41
Sample mean 97.5 98.1
Sample standard deviation 17.5 19.2

  • Two independent means, normal distribution
  • Two independent means, student's-t distribution
  • Matched or paired samples, student's-t distribution
  • Two population proportions, normal distribution

B

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For questions [link] – [link] , use the following information.

An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a “biofeedback exercise program.” Six (6) subjects were randomly selected and the blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated after − before size 12{ left ( ital "after" - ital "before" right )} {} producing the following results: x ¯ d = − 10 . 2 size 12{ {overline {x}} rSub { size 8{d} } = - "10" "." 2} {} s d = 8 . 4 size 12{s rSub { size 8{d} } =8 "." 4} {} . Using the data, test the hypothesis that the blood pressure has decreased after the training,

The distribution for the test is

  • t 5 size 12{t rSub { size 8{5} } } {}
  • t 6 size 12{t rSub { size 8{6} } } {}
  • N ( − 10 . 2,8 . 4 ) size 12{N \( - "10" "." 2,8 "." 4 \) } {}
  • N ( − 10 . 2, 8 . 4 6 ) size 12{N \( - "10" "." 2, { { size 8{8 "." 4} } over { size 8{ sqrt {6} } } } \) } {}

A

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If α = 0 . 05 size 12{a=0 "." "05"} {} , the p size 12{p} {} -value and the conclusion are

  • 0.0014; There is sufficient evidence to conclude that the blood pressure decreased after the training
  • 0.0014; There is sufficient evidence to conclude that the blood pressure increased after the training
  • 0.0155; There is sufficient evidence to conclude that the blood pressure decreased after the training
  • 0.0155; There is sufficient evidence to conclude that the blood pressure increased after the training

C

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For questions [link] – [link] , use the following information.
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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