12. Naim and Sham, senior agents at an airline security checkpoint, carry out advanced screening procedures for hundreds of randomly selected passengers per day. For a random sample of 38 passengers recently processed by Naim, the mean processing time was 124.5 seconds, with a standard deviation of 20.4 seconds. For a random sample of 45 passengers recently processed by Sham, the corresponding mean and standard deviation were 133.0 seconds and 38.7 seconds, respectively. Using the 0.03 level of significance, can we conclude that the population mean processing times for Naim and Sham could be same? Assume the normal populations with different variances.

14. A software company has produced two types of operating systems. For marketing purposes, a survey of users of the two operating systems is conducted. 31 users of operating system A record the average level of satisfaction of 77 on a 100-point scale, with a sample variance of 220. 51 users of operating system B have the average satisfaction level of 70 with a sample variance of 155. Assuming the population variances are equal, can we conclude that the level of satisfaction of operating system A is higher than system B?

15. Safety engineers at a manufacturing plant are evaluating two brands of 50-ampere electrical fuses for possible purchase and use in the plant. One of the performance characteristics they are considering is how long the fuse will carry 50-amperes before it blows. In a sample of 35 fuses from the Company A, the mean time was found to be 240 milliseconds, with a standard deviation of 50 milliseconds. In comparable tests of a sample of 31 fuses from the Company B, the mean time was 221 milliseconds, with a standard deviation of 28 milliseconds. Using the 0.10 level of significance and assume that the population variances are unequal, test whether the population mean times for fuses from the tow companies might be same.