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Thread: Hypothesis test of sample (yes/no) and proportions

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    Question Hypothesis test of sample (yes/no) and proportions




    Edit: I'm not sure whether this belongs in statistics or probability forum.

    Hi guys,

    I' prepping for exams with old exam questions and I'm stuck on the following:

    Info:
    More and more hotel guests are using apps to determine which hotel to stay at, and the most popular app was App X.
    A sample from 2014 showed that 125 of 200 hotel guests used App X to determine
    which hotel to stay at.

    Question:
    Test on a 5% level (alpha = 0.05), if above half of the hotel guests in 2014 used App X to pick a hotel.

    My proposed solution:

    H0 : ≤ 0.5
    H1 : > 0.5
    α = 0.05
    n = 200
    k = 101
    p = 125 / 200 = 0.625

    If p-value is ≤ α, then the null-hypothesis is rejected.
    If p-value is > α, then the null-hypothesis is accepted.

    0.0002 < 0.05, so we reject the null hypothesis and say with 95% confidence that above half of the hotel guests in 2014 used App X to pick their hotel.


    My question to talkstats:
    Is this solution above correct?

    (Less significant question): Given that the solution above is correct, can I with 99,9% confidence say that above half of the hotel guests in 2014 used App X to pick their hotel?
    I wrote with 95% confidence in the solution because the way I understand that question, 95% confidence is what they asked for, so I should only mention that.



    Then there is the follow-up question that really has me in doubt about what and which approach to use to solve it.

    Info for follow-up question:
    A similar study was done in 2012, where the sample showed that 77 out of 145 used App X to pick their hotel.

    Follow-up question:
    Test on 5% level, if the number of hotel guests using App X to pick their hotel has increased with more than 5% during those two years.


    My questions and doubts:
    What approach should I use?
    I am guessing that I can use hypothesis testing of two proportions, but I am in doubt about which proportions to use and how to write the null and alternative hypothesis.
    - And whether or not it is correct to use hypothesis testing of two proportions to solve the question.

    So I'm stuck and any hints or solutions is greatly appreciated.
    Last edited by BioEngineer; 05-26-2016 at 05:03 AM.

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