1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Population Proportion
  1. Population Model (Replies: 2)

  2. Population and limits (Replies: 2)

  3. Population model (Replies: 1)

Loading...