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Statistical inference — Question 13

QCAA 2023, Paper 2 · 4 marks

Q13 · 2023 · Technology-activeSimple familiar4 marks

QUESTION 13 (4 marks)

The wait time for customers put on hold when calling complaint departments is assumed to be normally distributed. A company claims that the mean wait time for their customers is 7.6 minutes. The following data represents the wait time (minutes) from a random sample of 12 customers who called the complaint department of this company.
8.312.79.17.310.35.48.510.76.912.57.211.9
------------------------------------
a)
Determine the mean of this data.
[1 mark]
b)
The standard deviation of this data is calculated to be 2.384 minutes. Use an approximate 95% confidence interval for the mean to evaluate the reasonableness of the company’s claim. Justify your decision using mathematical reasoning.
[3 marks]
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