How to Construct a Confidence Interval

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How to Construct a Confidence Interval Instructions on the left Instructions on the right pertain to means pertain to proportions 1. POPULATION a. Identify the parameter of interest: µ : Mean π : proportion Numerical (Measurement) Categorical (success-failure) b. Describe the variable in context with the problem: µ = mean of the amount of drying time of a π = proportion of people in the community who particular paint. prefer smoking 2. STATISTICAL METHOD a. Determine the confidence level (1 - ) and the level of significance . NOTE: If not specified, set the confidence to 0.95 (95%) and the level of significance to 0.05. b. Identify the required formula for the confidence interval: When σ known: x zcriticalvalue pp1 n p zcriticalvalue n When σ unknown: s x tcriticalv alue n 3. SAMPLE a. Calculate or identify the descriptive statistics: Descriptive statistics Descriptive statistics needed: needed: the sample proportion the sample mean sample size standard deviation sample size b. Check the conditions for normality: population is normal OR np 10AND n1 p 10 n ≥ 30 www.rit.edu/ASC Page 1 of 2 4. STATISTICAL RESULTS a. Find the required z or t critical value: z critical value: Same as z critical value information on the left. 1. Find 2 2. Take this value and locate it in the standard normal probability table and identify the z critical value. NOTE: Commonly used z critical value Confidence Level z critical value 2 90% .10 .05 1.645 95% .05 .025 1.960 99% .01 .005 2.576 t critical value: 1. Determine the degrees of freedom: df = (n - 1) 2. Use the appropriate confidence level and the df and locate the t critical value in the t critical value table. For example, Confidence Level df t critical value 90% 15 1.75 98% 7 3.00 95% 23 2.07 b. Compute the confidence interval based on formula in step 2. NOTE: Calculator shortcuts for the confidence interval: When σ known: Z-Interval 1-PropZInt When σ unknown: T-Interval 5. CONCLUSION Interpret the confidence interval in the context of the problem: Ex) There is 95% probability that the Ex) There is 95% probability that the proportion of mean drying time is between… people who prefer smoking is between… www.rit.edu/ASC Page 2 of 2 .

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