7 A market researcher is investigating the length of time that customers spend at an information desk. He plans to choose a sample of 50 customers on a particular day.
- He considers choosing the first 50 customers who visit the information desk.
Explain why this method is unsuitable.
The actual lengths of time, in minutes, that customers spend at the information desk may be assumed to have mean \(\mu\) and variance 4.8. The researcher knows that in the past the value of \(\mu\) was 6.0. He wishes to test, at the \(2 \%\) significance level, whether this is still true. He chooses a random sample of 50 customers and notes how long they each spend at the information desk. - State the probability of making a Type I error and explain what is meant by a Type I error in this context.
- Given that the mean time spent at the information desk by the 50 customers is 6.8 minutes, carry out the test.
- Give a reason why it was necessary to use the Central Limit theorem in your answer to part (c).
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