In the textbook Example 4.19, the author calculates confidence interval using sample mean +- margin of error, i.e., the interval is calculated as (2.78-1.96x0.256, 2.78+1.96x0.256). Then he concludes that the null value 3.09 is within the interval therefore it cannot be rejected.
But later on in the one-tailed examples, the confidence interval seems to be constructed with the null value being in the center, see Fig 4.13, 4.15, 4.16, 4.18. The author is saying that if null is true, it is unusual to see observed value outside the interval - null is rejected if observed sample mean is outside the interval (null + margin, null - margin).
If we use the same logic for Example 4.19, can we construct an interval (3.09-1.96x0.256, 3.09+1.96x0.256)? Then check if the sample mean 2.79 is within the interval?
In this example, it seems both ways work - they both are within those intervals. But is there a difference? Can both works in all cases?
In the textbook Example 4.19, the author calculates confidence interval using sample mean +- margin of error, i.e., the interval is calculated as (2.78-1.96x0.256, 2.78+1.96x0.256). Then he concludes that the null value 3.09 is within the interval therefore it cannot be rejected.
But later on in the one-tailed examples, the confidence interval seems to be constructed with the null value being in the center, see Fig 4.13, 4.15, 4.16, 4.18. The author is saying that if null is true, it is unusual to see observed value outside the interval - null is rejected if observed sample mean is outside the interval (null + margin, null - margin).
If we use the same logic for Example 4.19, can we construct an interval (3.09-1.96x0.256, 3.09+1.96x0.256)? Then check if the sample mean 2.79 is within the interval?
In this example, it seems both ways work - they both are within those intervals. But is there a difference? Can both works in all cases?