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Statistical inference — Question 19

QCAA 2023, Paper 2 · 7 marks

Q19 · 2023 · Technology-activeComplex unfamiliar7 marks

QUESTION 19 (7 marks)

The height of Year 9 students at a school is assumed to be normally distributed with a population mean height of μ\mu cm. A teacher at the school measured the height of all the students in her Year 9 class. This data was used to calculate an approximate 95% confidence interval for μ\mu of (163.7,166.9)(163.7,166.9) cm. The teacher repeated the procedure using data from another Year 9 class. Although this class had the same number of students, its data produced an approximate 95% confidence interval for μ\mu of (167.8,172.4)(167.8,172.4) cm. Using the same data, the teacher recalculated the approximate confidence intervals for μ\mu for each class using a confidence level of xx%. She observed that the upper bound of the confidence interval from her Year 9 class now equalled the lower bound of the confidence interval from the other class. Determine xx.
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