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Homework Help: Population Proportion

  1. Sep 11, 2009 #1
    Each of a group of 20 tennis players is given 2 rackets, 1 having nylon strings and the having gut strings. After several weeks of playing with 2 rackets, each player will be asked to state a preference for one of 2 types of strings. Let p denote the proportion of all such players who prefer gut, and let X be number of players in the sample who prefer gut. Because gut is more expensive consider the null hypotheses that at most 50 % of all such players prefer gut. We simplify this to Ho: p= .5 planning to reject Ho only if sample evidence strongly favors gut strings.

    a) Which of the rejection regions {15,16,17,18,19,20}, {0,1,2,3,4 5} or {0,1,2,3,17,18,19,20} is most appropriate and why are the other two not appropriate?

    b)What is the probability of a type I error for the chosen region of part a? Does the region specify a .05 test? Is it the best level .05 test?

    d) If 13 out of the 20 players prefer gut, should Ho be rejected using a significance level of .10?

    My breakdown of the problem is as follows:
    Ho: p=.5
    Ha: p<.5

    Looking at part d [tex]\hat{p}[/tex] = 13/20=0.65

    T[tex]\alpha[/tex]=T 19,.1 = 1.328

    T=[tex]\frac{.65-.5}{\sqrt{\frac{.5(1-.5}{20}}}= 1.342[/tex]

    1.342 > .5, We reject Ho

    We can conclude that that the gut string is more preferable than the nylon string.

    What do I do with part a) and am I on track with part d bc it seems as though I should be solving for p<.5
  2. jcsd
  3. Sep 12, 2009 #2
    Any help...how would I start out figuring these rejection regions?
  4. Sep 15, 2009 #3
    Alright is there any suggestions for part a? A formula? I know it has to do with Bernoulli and it is 50-50.
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