What would the hypotheses be for the test of differences in mean operating cost for private vs publicly owned bus companies?

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BlackTom AI · Accepted Answer

Let's parse the question: we are dealing with a test of differences in mean operating costs between two groups, private vs publicly owned bus companies. The null hypothesis (H0) in such two-sample mean difference tests typically states that the two population means are equal, while the alternative hypothesis (H1) states that they are not equal (two-tailed) unless there is a specific directional hypothesis.

Option a: 'a. ( H0: μprivate ≠ μpublic  H1: μprivate = μpublic' This flips the logical roles: stating a null hypothesis of inequality and an alternative of equality reverses the standard structure and would not be appropriate for a standard two-sample test of means. It is conceptually inconsistent with how hypotheses are usually formulated.

Option b: 'b. H0: μprivate = μpublic  H1: μprivate < μpublic' This is a one-sided test proposing that private costs are strictly less than public costs. Unless the research question explicitly posits a directional claim (private should be cheaper) and you have prior evidence, this is not the general form for testing any difference.

Option c: 'c. H0: μprivate = μpublic  H1: μprivate > μpublic' Similar to option b, this is a one-sided alternative but in the opposite direction (private costs greater than public costs). Again, without a stated directional hypothesis, this is not the standard default form.

Option d: 'd. H0: μprivate = μpublic  H1: μprivate ≠ μpublic' This represents a two-tailed test of equality vs difference between the means, which is the conventional setup when testing for any difference in means without a specified direction. It captures the possibility that either group could have higher or lower costs.

In summary, among the given choices, option d aligns with the conventional two-sample mean difference test framework: H0 asserts equality of means, and H1 asserts that the means are different (not equal). The other options impose a directional alternative or misuse the null/alternative roles, which would be inappropriate unless a specific directional hypothesis was pre-specified and justified.

MCD2080 - T1 - 2025 Lecture Lesson 2 (Week 6)

What would the hypotheses be for the test of differences in mean operating cost for private vs publicly owned bus companies?

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