1. Two machines are supposed to be producing steel bars of approximately the same length. A sample of 35 bars from one machine has an average length of 37.013 inches, with a standard deviation of 0.095 inches. For 38 bars produced by the other machine, the corresponding figures are 36.974 inches and 0.032 inches. Using the 0.05 level of significance, test the null hypothesis that the population means are equal. Using the appropriate statis- tical table, what is the approximate p-value for this test? Construct and interpret the 95% confidence interval for the difference between the population means.
2. Observing a sample of 35 morning customers at a convenience store, a researcher finds their average stay in the store is 3.0 minutes, with a standard deviation of 0.9 minutes. For a sample of 43 afternoon customers, the mean and standard deviation were 3.5 and 1.8 minutes, respectively. Using the 0.05 level of significance, determine whether the population means could be equal. Construct and interpret the 95% confidence interval for the differ- ence between the population means.