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10.1 Homework  (Page 7/7)

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The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals.

Western Eastern
Los Angeles 9 D.C. United 9
FC Dallas 3 Chicago 8
Chivas USA 4 Columbus 7
Real Salt Lake 3 New England 6
Colorado 4 MetroStars 5
San Jose 4 Kansas City 3

Conduct a hypothesis test to determine if the Western Reserve Division teams score, on average, fewer goals than the Eastern Reserve Division teams. Subscripts: 1 Western Reserve Division ( W ); 2 Eastern Reserve Division ( E )

The exact distribution for the hypothesis test is:

  • The normal distribution.
  • The student's-t distribution.
  • The uniform distribution.
  • The exponential distribution.

B

If the level of significance is 0.05, the conclusion is:

  • There is sufficient evidence to conclude that the W Division teams score, on average, fewer goals than the E teams.
  • There is insufficient evidence to conclude that the W Division teams score, on average, more goals than the E teams.
  • There is insufficient evidence to conclude that the W teams score, on average, fewer goals than the E teams score.
  • Unable to determine.

C

Questions [link] – [link] refer to the following.

Neuroinvasive West Nile virus refers to a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test. (Source: http:// http://www.cdc.gov/ncidod/dvbid/westnile/index.htm )

  • “2011” subscript: 2011 group.
  • “2010” subscript: 2010 group

This is:

  • a test of two proportions
  • a test of two independent means
  • a test of a single mean
  • a test of matched pairs.

A

An appropriate null hypothesis is:

  • p 2011 ≤ p 2010 size 12{p rSub { size 8{ ital "drugless"} }<= p rSub { size 8{ ital "drug"} } } {}
  • p 2011 ≥ p 2010 size 12{P rSub { size 8{ ital "drugless"} }>= P rSub { size 8{ ital "drug"} } } {}
  • μ 2011 ≤ μ 2010 size 12{μ rSub { size 8{ ital "drugless"} }>= μ rSub { size 8{ ital "drug"} } } {}
  • p 2011 > p 2010 size 12{P rSub { size 8{ ital "drugless"} }>P rSub { size 8{ ital "drug"} } } {}

A

The p size 12{p} {} -value is 0.0022. At a 1% level of significance, the appropriate conclusion is

  • There is sufficient evidence to conclude that the proportion of people in the United States in 2011 that got neuroinvasive West Nile disease is less than the proportion of people in the United States in 2010 that got neuroinvasive West Nile disease.
  • There is insufficient evidence to conclude that the proportion of people in the United States in 2011 that got neuroinvasive West Nile disease is more than the proportion of people in the United States in 2010 that got neuroinvasive West Nile disease.
  • There is insufficient evidence to conclude that the proportion of people in the United States in 2011 that got neuroinvasive West Nile disease is less than the proportion of people in the United States in 2010 that got neuroinvasive West Nile disease.
  • There is sufficient evidence to conclude that the proportion of people in the United States in 2011 that got neuroinvasive West Nile disease is more than the proportion of people in the United States in 2010 that got neuroinvasive West Nile disease.

D

Questions [link] and [link] refer to the following:

A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four (4) new students. She records their 18-holes scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as follows.

Player 1 Player 2 Player 3 Player 4
Mean score before class 83 78 93 87
Mean score after class 80 80 86 86

This is:

  • a test of two independent means
  • a test of two proportions
  • a test of a single proportion
  • a test of matched pairs.

D

The correct decision is:

  • Reject H o size 12{H rSub { size 8{o} } } {}
  • Do not reject H o size 12{H rSub { size 8{o} } } {}

B

Questions [link] and [link] refer to the following:

Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The “day” subscript refers to the statistics day students. The “night” subscript refers to the statistics night students.

An appropriate alternate hypothesis for the hypothesis test is:

  • μ day > μ night size 12{μ rSub { size 8{8:"30"} }>μ rSub { size 8{"11":"30"} } } {}
  • μ day < μ night size 12{μ rSub { size 8{8:"30"} }<μ rSub { size 8{"11":"30"} } } {}
  • μ day = μ night size 12{μ rSub { size 8{8:"30"} } =μ rSub { size 8{"11":"30"} } } {}
  • μ day ≠ μ night size 12{μ rSub { size 8{8:"30"} }<>μ rSub { size 8{"11":"30"} } } {}

D

A concluding statement is:

  • There is sufficient evidence to conclude that statistics night students mean on Exam 2 is better than the statistics day students mean on Exam 2.
  • There is insufficient evidence to conclude that the statistics day students mean on Exam 2 is better than the statistics night students mean on Exam 2.
  • There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.
  • There is sufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.

C
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Source:  OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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