QUESTION 1

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight this year.

To accomplish this, the records of n=264 flights are randomly selected and the number of unoccupied seats is noted for each of the flights in the sample. The sample mean number of unoccupied seats will be used as an estimate for the average number of unoccupied seats for all flights to be completed this year, this had value 7.26. The number of unoccupied seats vary between flights by a standard deviation of 2.2.

Estimate the value of the population mean , i.e. the mean number of unoccupied seats per flight of all flights this year.Fill in the blanks in the following:

• An estimate of the population mean is.
• The standard error is.
• The distribution is (examples: normal / t12 / chisquare4 / F5,6).
• For a 95% confidence interval the distributional cut-off is.

It is quite likely that the true mean number of unoccupied seats for all flights is between and .

QUESTION 2

A media company claimed that the average number of unoccupied seats per flight for this airline company is equal to 10. Is there evidence to support this claim ?

a. No - the claim thatthe averagenumber of unoccupied seats per flight for this airline company,,is equal to 10 is unlikely according to the plot of the sampled values in question 2.

b. Yes - the claim thatthe averagenumber of unoccupied seats per flight for this airline company,,is equal to 10 is likely since this value is in the confidence interval calculated in question

c. No - the claim thatthe averagenumber of unoccupied seats per flight for this airline company,,is equal to 10 is unlikely since this value is not in the confidence interval calculated in question

d. Yes - the claim thatthe averagenumber of unoccupied seats per flight for this airline company,,is equal to 10 is likely according to the plot of the sampled values in question 2.

QUESTION 3

The following figure displays a histogram of the recorded number of unoccured seats for the sample of flights discussed in the previous question. Based on the plot would you have any reservations about the validity of the inference carried out in the previous question? 50 40- 30- Frequency 20- 10- 10 15 20 25 number unoccupied seats per flight O a. No - The plot shows that the sample is skewed with an outlier and as a result it is likely that the sample was selected from a population of flights whose number of unoccupied seats is skewed and therefore not normally distributed. However the Central Limit Theorem applies in this case, and the sampling distribution is normally distributed for any popluation distribution. O b. Yes - The plot shows that the sample is skewed with an outlier and as a result it is likely that the sample was selected from a population of flights whose number of unoccupied seats is skewed and therefore not normally distributed. Therefore the assumption required to carry out the analysis, that the population be normally distributed, is not valid. O c. No - the plot shows that the sample has an approximatey normal distribution and so it is likely that the sample was selected from a population of flights whose number of unoccupied seats is normally distributed