1. A population has a variance of 625. How large a sample would be needed so that the mean would be within 4 of the population mean (95% confidence).
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2.
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A political candidate wishes to find the proportion of voters who support his party. How large a sample would he need to gauge his level of support to within 3% at a 99% confidence level? |
3. A candidate in an election wanted to estimate the proportion of all students in Year 10 to Year 12 at her school who favoured a change in the school hours. Of 100 students in her random sample, 72 favoured a change.
(i) Find a 90% confidence interval for the proportion of all students in year 10 to Year 12 who would favour the change.
(ii) How large would the candidate's sample need to be if the total length of the interval in part (i) was to be less than or equal to 0.2.
4. Steel sheets have weights with a standard deviation of 10 kg.
What sample size should be taken to estimate the mean weight to within 2 kg of the population value with a 95% level of confidence?
5. Previous surveys have revealed that 39% of households have access to the Internet.
What size of sample should be taken so that the sample proportion is within 4% of the true percentage at a 98% confidence level?
