IB Maths AI HL AI 4.4 Hypothesis testing and confidence intervals questions

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Question 1

Paper 1Medium6 marks

A parcel-delivery company defines its daily forecast error as

\text{actual number of parcels}-\text{forecast number of parcels}.

A random sample of 16 independent days has a mean forecast error of 18.4 parcels and a sample standard deviation of 12.0 parcels. The daily forecast errors may be modelled by a normal population, whose standard deviation is unknown.

(a)

State which distribution should be used to construct a confidence interval for the population mean forecast error, $\mu$

[1]

(b)

Calculate a 95% confidence interval for $\mu$ Give both endpoints to one decimal place.

[3]

(c)

The planning director claims that the forecasts are unbiased, so that $\mu=0$ Use your interval to comment on this claim and state the direction of any bias indicated.

[2]

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