Suppose a scheduled airline flight must average at least 60...

Suppose a scheduled airline flight must average at least $60 \%$ occupancy in order to be profitable. Occupancy rates were recorded daily for a regularly scheduled flight on each of 120 days, showing a mean occupancy per flight of $58 \%$ and a standard deviation of $11 \%$. a. If $\mu$ is the mean occupancy per flight and if the company wishes to determine whether or not this scheduled flight is unprofitable, give the alternative and the null hypotheses for the test. b. Does the alternative hypothesis in part a imply a oneor two-tailed test? Explain. c. Do the occupancy data for the 120 flights suggest that this scheduled flight is unprofitable? Test using $\alpha=.05$

Transcript

00:01 So our question says suppose a scheduled airline flight must have average at least 60 occupancy in order to be profitable.

00:07 Occupancy rates were recorded daily for a regular scheduled flight on each of 120 days, showing a mean occupancy per flight of 58 and a standard deviation of 11.

00:18 So the first question says if m is the main occupancy per flight and if the company wishes to determine whether or not this scheduled flight is unprofitable.

00:27 Give the alternative and the null hypothesis for this test.

00:30 So that's our first question so before we work on the first question or the whole question as a whole we have to list out the parameters so the population mean mu is equal to 60 the sample size n is a cost to 120 the sample mean x bar is equal to 58 and the sample standard deviation s is equal to we have that to be 11 so our first question is for us to state the null and alternative hypothesis now please listen the first sentence is that supposed to be 11 a scheduled airline flight most average at least 60 occupancy in order to be profitable at least means it starts from 60 so that means our null hypothesis is based on the fact that m is greater than or equals to 60 now there is something about the null and alternative hypothesis both sentences are they go against each other so if the null hypothesis is going towards the right then definitely the alternative hypothesis must go towards the left and also a the null hypothesis is most always include the equality sign so our alternative hypothesis will be based on the fact that mu is actually lesser than 60 so that been said the second question says that does the null hypothesis does the alternative hypothesis imply a one or a two tilt test from our alternative hypothesis we can say that it is towards the left so it implies a left tilt or a lower tail test which is also a one -tailed test so that being said the third question says that do the occupancy data for the 120 flights suggest that the shadow flight is unprofitable so you are supposed to perform our hypothesis test on our data so the next step is for us to state the p -value the decision rule rather that is going to make us accept or rejects did not hypothesis and i'll be making use of the p -value method in this case of us so it states that if our p -value is greater than alpha we are supposed to fail to reject the null hypothesis and if our p value is greater than alpha we are supposed to reject sorry if our p value is lesser than alpha rather if our p value is lesser than alpha we are supposed to reject the null hypothesis so that being said it's time to get the test statistics which will allow us to get the p value so our test statistics in this case can either be a z test or a t test but let's look at the sample size our sample size is 120 which is a sample size that is greater than 30 so since our sample size is far greater than 30 it obeys the central limit theorem hence that means our sampling distribution is approximately normal hence our test statistics is going to be a z test so we have the z is equal to x bar minus mil divided by s divided by the square root of n so x bar in this case is 58 minus our mil is equal to 60 divided by our s is 11 divided by the square root of n and that is 120.

03:37 So 58 minus 60 that gives us minus 2 divided by so i will be using our calculator to get the value of 11 divided by the square root of 120.

03:48 So we have that 11 divided by the scroll out of 120 and that gives us 1 .00415.

04:01 And we'll do the math z is equal to so minus 2 divided by 1 .045 and that gives us minus 1 .045 and that gives us minus 1 .0.

04:10 So our test statistics is minus 1 .99...

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