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A survey of passengers travelling from airports in London showed that passengers disliked waiting at security control. Two airports in London decide to investigate the issue.

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Heathrow Airport asked a random sample of 16 passengers to record how long they waited at security control. The mean waiting time for the sample was 31 minutes with a standard deviation of 7 minutes.

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London City Airport asked a random sample of 10 passengers to record the same information. The mean waiting time for the sample was 26 minutes with a standard deviation of 8 minutes.

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Assume that the waiting times for all passengers are normally distributed. Use a two sample t-test with a 5% significance level to determine if there is a    difference in waiting times at Heathrow Airport and London City Airport.

Fill the by writing appripriate words

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The null hypothesis is

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There is no difference between the wait times at Heathrow and City airports

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There is difference between the wait times at Heathrow and City airports

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The alternative hypothesis is:

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There is no difference between the wait times at Heathrow and City airports

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There is  difference between the wait times at Heathrow and City airports

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Write down the number of degrees of freedom

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Write down the critical value to 2 decimal places at 5% significane level.

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Calculate the pooled sample standard deviation Sp to 2 decimal places.

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Calculate the test statistics to 2 decimal places.

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What is the conclusion?

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A coffee shop chain would like to reduce costs by introducing a new cheaper blend of coffee, but before they make the change, they decide to test how many customers will notice the difference. They test the new blend in two locations; Birmingham and Southampton. 2000 customers took part in the survey. 800 from Birmingham and 1200 from Southampton.

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96 of the customers in Birmingham answered ‘Yes I can taste the difference’.

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240 of the customers in Southampton answered ‘Yes I can taste the difference’.

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Determine the probability that a customer will not taste the difference. Give your answer to (3 decimal places).

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Given that a customer answers ‘yes I can taste the difference’ what is the probability that they are from Birmingham? Give your answer to (3 decimal places).

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The coffee shop believes that only 5% of customer will switch to a competitor if they introduce the cheaper coffee blend. The coffee shop chain take a sample of 50 customers.

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Calculate the probability that exactly 4 customers in this sample state that they will switch to a competitor. Give your answer to (3 decimal places).

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State which probability distribution you used in part c).

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State two assumptions of that distribution.

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