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Repeat given Exercise using the z-test approximation to the unequal-variances t-test.

Exercise
Fred and Martina, 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 30 passengers recently processed by Fred, the mean processing time was 124.5 seconds, with a standard deviation of 20.4 seconds. For a random sample of 36 passengers recently processed by Martina, the corresponding mean and standard deviation were 133.0 seconds and 38.7 seconds, respectively. Using the 0.05 level of significance, can we conclude that the population mean processing times for Fred and Martina could be the same?

Using the appropriate statistical table, what is the most accurate statement we can make about the p-value for the test? Construct and interpret the 95% confidence interval for the difference between the population means.

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