Consumer opinion study

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Question 3 (4 + 2 = 6 marks)
(a) In a sample of 100 items from a production line, 14 are defective. Use these sample data to construct a 99% confidence interval for the true proportion of all items that are defective.
(b) A national survey research firm has past data that indicate that the interview time for a consumer opinion study has a standard deviation of 16 minutes. How large a sample should be taken if the firm wants to estimate the mean interview time to within 2.5 minutes or less with 95% confidence?
Question 4 (6 marks)
A city planner working on bike tracks needs information about local bicycle commuters. He designs a questionnaire. One of the questions is how many minutes it takes the rider to pedal from home to his or her destination. A random sample of local bicycle commuters yields the following times.
21 19 24 31 29 29 21 15 27 23 38 31 30 26 14
Assume that the times are normally distributed. At a 5% level of significance, can we conclude that the mean commuting time of all local bicycle commuters in the city is more than 20 minutes?
END OF TEST PAPER