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8.1B Confidence Interval Example The gas mileage for a certain model of car is known to have a standard deviation of 5 mi/gal. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gal. Construct a 95% confidence interval for the mean gas mileage for this car model. “Inference Toolbox” Steps for constructing a confidence interval: Step 1: Identify the population of interest and the parameter you want to draw conclusions about. We are interested in estimating the mean gas mileage μ for this car model. Step 2: Choose (State) the appropriate inference procedure. Verify the conditions for using the selected procedure. STATE: We will construct a one-sample z confidence interval. CONDITIONS: RANDOM: The problem states that the 64 cars compose a SRS. NORMAL: The sample size is large (64). INDEPENDENT: 10% Rule – 64*10 = 6400. It is reasonable to believe that there is at least 6400 cars manufactured for a specific model. All the conditions are met. Step 3: If the conditions are met, carry out the inference procedure. CI = Estimate +/- Margin of Error CI = x-bar ± z* σ/ √n 27.5 ± 1.96 ∙ 5 / √64 27.5 ± 1.225 (26.275, 28.725) Step 4: Interpret your results in the context of the problem. We are 95% confident that the interval from 26.275 to 28.725 mi/gal captures the true mean gas mileage for a certain model of car. The volume of bottles of soda from an assembly line is known to have a standard deviation of 0.076 liters. A quality control inspector tested the volume of 36 randomly selected bottles of soda from the assembly line and obtained a mean volume of 1.98 liters. Find the 98% confidence interval for the mean volume of all bottles from the assembly line.