A fish-processing company is concerned about the shelf life of its new cat food. A sample examined in Halifax, Nova Scotia (n = 35) had an acceptable mean shelf life of 13 months, with a standard deviation of 1.44 months. But a second sample, examined in Dartmouth, Nova Scotia (n - 40), had a mean shelf life of only 11 months, with a standard deviation of 1.52 months. The manager in Dartmouth claims that there is no significant difference between these two means.
a. Test her claim at the 0.05 level of significance. Based on the result, should the operation in Dartmouth be subjected to a special review?
b. Construct a 95% confidence interval for the difference between the population means (μ1 - μ2), where μ1 is the mean shelf life of cat food in Halifax and μ2 is the mean shelf life of cat food in Dartmouth. Do the confidence interval limits contain 0? Does this suggest that there is not a significant difference between the two population means?