Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    8
    ReputationRep:
    Hi, how do I go about solving this?
    I've seen the mark scheme but don't get it so I will need explanation at all steps.

    Name:  heolp.jpg
Views: 63
Size:  120.1 KB

    So far this is what I've thought:

    Ho: p=0.65
    H1: p<0.65

    X~B(2n,0.65)

    Since we want to reject,
    P(X>=n)<0.15
    so
    P(X<=n-1)>0.85

    and I can't use tables to solve that?
    Offline

    22
    ReputationRep:
    (Original post by DQd)
    Ho: p=0.65
    H1: p<0.65
    Absolutely, well done.

    X~B(2n,0.65)
    On the right track.

    Since we want to reject,
    P(X>=n)<0.15
    so
    P(X<=n-1)>0.85

    and I can't use tables to solve that?
    That's where you went wrong. Since this is a lower-tailed test or whatever it's called you need P(X <= n) > 0.15 -- then you need to do it by inspection. Remember you want the smallest n such that the test is rejected.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Zacken)
    That's where you went wrong. Since this is a lower-tailed test or whatever it's called you need P(X <= n) > 0.15 -- then you need to do it by inspection. Remember you want the smallest n such that the test is rejected.
    Can I ask why we use that and why what I posted doesn't work?

    "
    P(X>=n)<0.15
    so
    P(X<=n-1)>0.85
    "

    Doesn't this mean that the probability of 'x is = to or more than the actual number (n) that agreed to the shopping mall' is less than 15%, and in that case it would be rejected and that's what we need?

    Also I don't get how to use the tables to satisfy
    P(X <= n) > 0.15
    and
    x~B(2n, 0.65)

    Mark scheme says x~b(18,0.65) (n=9) but doesn't x~b(6,0.65) (n=3) also work?
    P(x<=3)=0.3529 which >0.15??
    Offline

    22
    ReputationRep:
    (Original post by DQd)
    Can I ask why we use that and why what I posted doesn't work?
    I'm glad you are.

    Think back to your definition of a hypothesis test, it's a lower-tailed one. For it to be rejected, we need substantial evidence that the proportion of people is less than 65%.

    Anywho, for the hypothesis to fail, you need to have P(X <= n) < 15% because that's saying that if (assuming that X ~ B(2n, 0.65), i.e: assuming that the proportion is 65%) then if the probability that there are less than n people agreeing is smaller than the significance level and hence the null hypothesis is rejected. You see what I'm getting at? Here's a video about hypothesis testing with the binomial distribution that you might find helpful for understanding.

    Think about it, X = 0 is the worst case, nobody agrees even though the claim says that 65% agrees. X=1 is also bad, all the way up to X=n is bad.

    BTW, typo in my above post - should be P(X <= n) < 15% which is why n=9 is the smallest value. Sorry.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by Zacken)
    I'm glad you are.

    Think back to your definition of a hypothesis test, it's a lower-tailed one. For it to be rejected, we need substantial evidence that the proportion of people is less than 65%.

    Anywho, for the hypothesis to fail, you need to have P(X <= n) < 15% because that's saying that if (assuming that X ~ B(2n, 0.65), i.e: assuming that the proportion is 65%) then if the probability that there are less than n people agreeing is smaller than the significance level and hence the null hypothesis is rejected. You see what I'm getting at? Here's a video about hypothesis testing with the binomial distribution that you might find helpful for understanding.

    Think about it, X = 0 is the worst case, nobody agrees even though the claim says that 65% agrees. X=1 is also bad, all the way up to X=n is bad.

    BTW, typo in my above post - should be P(X <= n) < 15% which is why n=9 is the smallest value. Sorry.
    It all works when I use 'P(X <= n) < 15%' .

    It makes more sense to be less than when I think about the reject region rather than use words, since if it is a smaller probability than 15% it will fit in the region.

    Still can't get my head around:
    "if the probability that there are less than n people agreeing is smaller than the significance level and hence the null hypothesis is rejected. "

    Because I'm thinking if the chance less than n people agree is small, the chance of 'at least 65%' is true goes up.

    The mark scheme is pretty useless, but is it wrong because it uses more than?
    Name:  heolp.jpg
Views: 47
Size:  102.2 KB
    Offline

    22
    ReputationRep:
    (Original post by DQd)
    It all works when I use 'P(X <= n) < 15%' .

    It makes more sense to be less than when I think about the reject region rather than use words, since if it is a smaller probability than 15% it will fit in the region.

    Still can't get my head around:
    "if the probability that there are less than n people agreeing is smaller than the significance level and hence the null hypothesis is rejected. "

    Because I'm thinking if the chance less than n people agree is small, the chance of 'at least 65%' is true goes up.

    The mark scheme is pretty useless, but is it wrong because it uses more than?
    Name:  heolp.jpg
Views: 47
Size:  102.2 KB
    Nah, the markscheme seems to be using the "accept" region, notice how it picks the first p = 0.13597 that's <= 15%? I'll get back to your other questions in a bit, gotta go now
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you rather give up salt or pepper?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.