1 (b). A survey of a random sample of 250 car commuters indicates that 80 would switch to commuting by public transport if they had to pay at least $10 per week for parking at their work places.
(i) Using a 95% confidence level, calculate the confidence interval for the proportion of the commuters who might be expected to change to using public transport for the journey-to-work.
(ii) Comment on the relationship between sample size and margin of error.
(c) Suppose we want to estimate, with 95% confidence, the percentage of commuters who would change to using public transport for the journey-to-work with a margin of error of +-3%. How large a sample of people will need to be taken:
(i) A preliminary estimate suggests that the true percentage is about 32%.
(ii) No preliminary estimate is available.
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Please see the attachments.
95% Confidence Interval for proportion is given by
where p = x/n = 80/250 = 0.32
Confidence Interval Estimate for the Mean
Sample Size 250
Number of Successes 80
Confidence Level 95%
Sample Proportion 0.32
Z Value -1.959963985
The solution provides step by step method for the calculation of confidence interval and sample size for population proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.