Question: We use hypothesis testing to help make decisions. In contrast, we use confidence intervals to tell us how reliable an estimate of some quantity is, for example a mean. Although confidence intervals are most commonly applied to means, we can also calculate confidence intervals for variances and other functions of random variables. We use similar mathematical reasoning for both hypothesis testing and confidence intervals.

1. Suppose we are constructing a bridge and need to order steel cable. We are considering three brands of cable. For each cable brand, the manufacturers supply us the mean and variance of the tensile strength (the amount of weight that is needed to cause the cable to break). The means and variances are based on a sample size of 10 for all three cable brands. Calculate t distribution based 95% confidence intervals for each cable brand. Note I have given you the sample variance not the variance of \[\bar{X}\] .

   Cable Brand	\[\bar{X}\]	s 2	Lower 95% Confidence Interval	Upper 95% Confidence Interval
   1	1056 kg	45,847 kg 2	902.828288	1209.17171
   2	1082 kg	74,298 kg 2	887.010302	1276.9897
   3	1132 kg	123,456 kg 2	880.649817	1383.35018

2. Which of the three cable brands do you think would make the safest bridge? Why?

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