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Statistical inference — Question 11

QCAA 2024, Paper 2 · 4 marks

Q11 · 2024 · Technology-activeSimple familiar4 marks

QUESTION 11 (4 marks)

A company claims that the mean battery life of their latest model of smartphone is 9.5 hours.
To test this claim, the battery lives of a random sample of 40 of the smartphones were measured. A sample mean of 9.31 hours and a standard deviation of 0.52 hours were calculated from this data.
a)
Determine an approximate 95% confidence interval for μ\mu. Give your answer to at least two decimal places.
[1 mark]
b)
Determine an approximate 99% confidence interval for μ\mu. Give your answer to at least two decimal places.
[1 mark]
c)
A manager comments that either confidence interval could be used to support the company’s claim. Use your results from Questions 11a) and 11b) to evaluate the reasonableness of the manager’s comment. Justify your decision using mathematical reasoning.
[2 marks]
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