EXAMPLE An insurance company has the business objective of reducing the amount

Example an insurance company has the business

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EXAMPLE: An insurance company has the business objective of reducing the amount of time it takes to approve applications for life insurance. Suppose you want to estimate, with 95 % confidence, the population mean processing time to within 4 days. On the basis of a study conduction the previous year, you believe that the standard deviation is 25 days. Determine the sample size needed. ? ? = ? ? 2 2 ? 2 ??? 2 , ? ? 2 = ? .05 2 = ? .025 = 1.96 1.96 ¿ 25 ¿ ¿ ? ? = ? ? 2 2 ? 2 ??? 2 = ¿ Therefore, you should select a sample of 151 applications. **Always round up to the next integer. STAT 206
Sample Size Determination for Proportion ??? = ? ? 2 ^ ? ( 1 ^ ? ) ? ????? ??? ? ? ? = ? ? 2 2 ? ( 1 ? ) ??? 2 where, = population proportion = is the critical value from the standardized normal distribution MOE = is the margin of error(sampling error) **when you have no prior knowledge of set = 0.50 STAT 206
EXAMPLE: Suppose the auditing procedures require you to have 95 % confidence in estimating population proportion of sales invoices with errors to within 0.07. The results from the past months indicate that the largest proportion has been no more than 0.15. Determine the sample size needed. **Always round up to the next integer . STAT 206
EXAMPLE: You want to have 90 % confidence in estimating population proportion of office workers who respond to email within an hour to within 0.05. Because you have not previously undertaken such a study, there is no information available from past data. Determine the sample size needed. ? ? = ? ? 2 2 ? ( 1 ? ) ??? 2 , ? ? 2 = ? .10 2 = ? .05 = 1.645 1.645 ( ¿¿ 2 ) ( 0.50 ) ( 0.50 ) .05 2 = 270.6 ? = ? ? 2 2 ? ( 1 ? ) ??? 2 = ¿ Therefore, you should select a sample size of 271. **Always round up to the next integer. STAT 206
Ethical Issues A confidence interval estimate (reflecting sampling error) should always be included when reporting a point estimate. The level of confidence should always be reported. The sample size should be reported. An interpretation of the confidence interval estimate should also be provided. STAT 206

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