Notes 8.3: Confidence Intervals with Means



Learning Target Predict Mean Parameter (?) with Statistic (x?) ? I can determine the confidence interval for means ?When we do any confidence interval we are using estimation we are using statistics (our point estimate) to predict parameters (within a certain range or interval).The process is the same as in 8.2, except instead of proportions we want to use our estimate of x? to predict ?.The values for z* are used, based on the confidence level.Values for z* make sense when the data is approximately normal. To check to see if our sampling distribution is approximately normal when using means, check this condition: Conditions for normal distributions with means: n > 30When n is at least 30, then the data is approximately normal.To compute the confidence interval we use the same “general” formula, but plug in values for means (instead of proportions): Confidence Interval = Statistic + (critical value) (standard deviation of statistic) = x? + (z*) (standard deviation of statistic)The formula for the standard deviation is calculated based on the sample size. The larger the sample size, the smaller the spread. When you look at the formula, this should make sense (because the standard deviation is divided by n). Standard deviation of the statistic = σnTo do a confidence interval, follow the steps: (ICCI)I: Identify State the statistic(s) you have and the parameter that you are trying to predictC: Check conditions Is the sample unbiased (SRS)?Check for normal: n > 30 C: Calculate Find:Standard deviation (sketch curve)z*Confidence interval using the formulaI: Interpret in context Write a sentence using the words that describe what the problem was about.Example 1: The mean systolic blood pressure for a SRS of 37 men is a study is x? = 114.9 with σ = 9.3. Find the mean systolic blood pressure for all men at a 98% confidence level.Identify: What statistic(s) do you have and what parameter are you looking for?Conditions: Check for unbiased and normalCalculate: Standard Deviation (use formula) Find z* value for the 98% confidence interval: ______________ Confidence Interval (use formula) Interpret: Using a 98% confidence interval, I predict the true mean systolic blood pressure of all men is from _________________ to ______________________ .? I can calculate and explain margin of error for confidence intervals with means ?The confidence interval equation using the statistic for means is (x?) + (z*)(standard deviation of statistic).Margin of Error: The “+ “ part of the equation This is the amount of “error” in either direction, that’s why the + What formula would you use if you were looking for the margin of error (instead of the entire interval)? Margin of error (the + part) = Example 2: A SRS of 50 middle school girls took an IQ test and the mean score of this group was 100, with σ = 8.Find the margin of error at a 90% confidence.Find the margin of error at a 95% confidence.Find the margin of error at a 99% confidence.As the confidence increases, what happens to the margin of error? ................
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