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

1. ## 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 : µ ≤ 0.5
H1 : µ > 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.

 Tweet

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts