Airlines regularly overbook flights as past experience has...

Airlines regularly overbook flights as past experience has shown that 5% of booked passengers do not show up for their flights. Following some passenger complaints, one airline took a random sample of all booked tickets in the past year and found out whether or not the passengers had actually shown up for their flights. a) Formulate the appropriate null and alternative hypotheses for the test and give the rejection region for a significance level of 1%. b) Of 1000 bookings samples it was found that 34 passengers did not show up. Find the p-value of the test. c) What would you conclude from this test? d) Construct a 99% upper bound on the proportion of passengers who do not show up for their flights based on this data.

Transcript

00:01 Now, here in this question, we have some, we look at some airlines, right? some past experience shows that 5 % of passengers do not show up for the flights, right? then your company decided to test this hypothesis, to test this claim, right? so they basically took a sample of 100 bookings, right? so they took a sample 100 bookings and they found that 34 of them actually did not show up.

00:36 So you're asked to test the hypothesis at alpha equals 1 % significance level, right? so the non -hypothesis obvious is that the actual proportion, population proportion, a passenger do not show up, which i'm going to call a mirror.

00:54 And obviously should be, according to the test, of course, according to the question, should be less than 5 %, right? and then the alternative hypothesis, of course, is that muo actually larger than 5%.

01:10 And then the test, the statistic i'm going to use is denote, right? and denot, obviously, is just, is of course given by the sample proportion.

01:24 The sample proportion i'm going to call a p, and that's actually given by 34 over 1 ,000.

01:29 So clearly there is just, it's 34 over 1 ,000.

01:36 So it's clearly much less than the claimed 5%.

01:41 So that's actually only, so you look at the test statistic.

01:45 Of course, it's actually 34.

01:49 I would like to basically look at, i don't want to use 34.

01:56 Per year, i would like to look at 5 % minus p, right, which is 34 over 1 ,000.

02:02 And that's clearly it's just 3 .4%, right? right, just 3 .4 % actually.

02:13 And divided by, of course, the standard deviation, which is actually given by p times 1 minus p.

02:21 So that's 3 .4 % times 1 minus 3 .4%.

02:25 That's actually 96 .6%.

02:28 And divided by the sample size, which is one something, right? and if you do the calculation, you'll find this to be given by 2 .79...

Question

Please give Ace some feedback