Go Fast Airlines provides internal flights in Ireland, short haul flights to Europe and long haul flights to America and Asia - Leaving Cert Mathematics - Question 7 - 2013
Question 7
Go Fast Airlines provides internal flights in Ireland, short haul flights to Europe and long haul flights to America and Asia. On long haul flights the company sells... show full transcript
Worked Solution & Example Answer:Go Fast Airlines provides internal flights in Ireland, short haul flights to Europe and long haul flights to America and Asia - Leaving Cert Mathematics - Question 7 - 2013
Step 1
Explain what is meant by a stratified random sample.
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Answer
A stratified random sample is a sampling method where the population is divided into distinct subgroups, or strata, that share similar characteristics. Random samples are then drawn from each stratum to ensure that all segments of the population are represented proportionally in the overall sample.
Step 2
Write down 4 different passenger groups that the company might have included in their sample.
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Long haul economy class passengers.
Long haul business class passengers.
Long haul executive class passengers.
Short haul passengers.
Step 3
What is the probability that a passenger selected at random from this sample had his/her flight delayed?
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The probability that a passenger had his/her flight delayed can be calculated as:
P(Delayed)=1000231=0.231
Step 4
What is the probability that a passenger selected at random from this sample was not satisfied with the overall service?
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The probability that a passenger was not satisfied is:
P(NotSatisfied)=1000238=0.238
Step 5
Do you agree with the employee? Give a reason for your answer.
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No, I do not agree with the employee. The probability of two events occurring simultaneously must account for their potential dependence; in this case, if a passenger's flight was delayed, they are likely to be dissatisfied with the service. Therefore, calculating the product of two independent probabilities is incorrect.
Step 6
Which of the graphs below do you think is most likely to represent the distribution of the weights of passenger baggage?
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Graph (ii) is most likely to represent the distribution of the weights of passenger baggage as it shows a normal distribution pattern, which is expected since most passengers are likely to have baggage weighing around the limit of 20 kg.
Step 7
Give a reason for your answer.
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The normal distribution indicates that the majority of baggage weights cluster around the mean, which likely corresponds with the weight limit set by the airline.
Step 8
Draw a sketch of the possible distribution of the ages of the passengers based on the data in the survey.
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The distribution might be positively skewed, suggesting that there are more younger passengers compared to older ones.
Step 9
Explain your answer.
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The median age being less than the mean suggests that there are a significant number of younger passengers, pulling the mean upwards.
Step 10
State the null hypothesis and conclusion regarding customer satisfaction.
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Null Hypothesis: The satisfaction level is unchanged with p = 0.70. After conducting the hypothesis test, the test statistic falls outside the 5% significance level range, therefore we reject the null hypothesis, concluding there is evidence that the claim is not valid.
Step 11
Is the manager correct?
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No, the manager is not correct. Halving the margin of error in survey results can only be achieved by increasing the sample size, and while surveying more passengers may improve reliability, it will not automatically half the margin of error.
Step 12
Calculate the correlation coefficient between passenger age and in-flight spend.
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The correlation coefficient (r) is calculated as:
r=0.88
Step 13
What can you conclude from the completed scatter plot and the correlation coefficient?
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There is a strong positive correlation between passenger age and in-flight spending, indicating that older passengers tend to spend more on in-flight services.
Step 14
Sketch the line of best fit in the completed scatter plot.
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The line of best fit would slope upwards, illustrating the positive relationship between age and in-flight spending.
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