Mathematical Methods ยท Unit 4 ยท Interval estimates for proportions ยท Confidence intervals for proportions
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A quality control manager samples 120 items from a production line and finds that 36 items are defective. Using \( z = 2 \), calculate the approximate margin of error for the proportion of defective items.
A market research company surveyed a random sample of 80 consumers to determine their preference for a new product. Of those surveyed, 32 consumers indicated they would purchase the product. (a) Determine the sample proportion. (1 mark) (b) Calculate the approximate margin of error using \( z = 2 \). Express your answer as a decimal correct to three decimal places. (2 marks) (c) Hence, determine the approximate confidence interval for the proportion of all consumers who would purchase the product. (1 mark)
A market research firm surveyed 225 customers to determine the proportion who prefer online shopping. The sample proportion who prefer online shopping was $\hat{p} = 0.48$. Using $z = 1.96$ for a 95% confidence level, calculate the approximate margin of error, correct to 4 decimal places.
A sample of 400 manufactured items contains 76 defective items. Using \(z = 1.96\), calculate the approximate margin of error for a 95% confidence interval for the proportion of defective items.