Three confidence intervals for the mean shear strength (in ksi) of anchor bolts of a certain type are computed, all from the same sample. The intervals are (4.01, 6.02), (4.20, 5.83), and (3.57, 6.46). The levels of the intervals are 90%, 95%, and 99%. Which interval has which level?

Answer:

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Three confidence intervals for the mean shear strength are computed, all from the same sample. The intervals are , , and . the levels of the intervals are 90%, 95%, and 99%.

Which interval has which level?

Lets plot the normal probability density function with mean and standard deviation

Figure 1: probability density function of normal random variable

From the figure, we can draw a conclusion about level, which is,

The higher the level, the wider the confidence interval and the lower the level, the narrower the confidence interval.

For example, 68% level is in the interval of and 99.7% level is in the interval of