A retail company introduced a new point-of-sale (POS) system with the aim of improving transaction efficiency. Historically, 80% of transactions were completed within 5 minutes with the old system. After implementing the new POS system, a survey of 200 transactions showed that 150 were completed within 5 minutes.

What is the correct usage for R's prop.test() to calculate the p-value for a two-sided hypothesis test to determine if there is a significant difference in the proportion of transactions completed within 5 minutes with the new POS system?

Question

A retail company introduced a new point-of-sale (POS) system with the aim of improving transaction efficiency. Historically, 80% of transactions were completed within 5 minutes with the old system. After implementing the new POS system, a survey of 200 transactions showed that 150 were completed within 5 minutes.

What is the correct usage for R's prop.test() to calculate the p-value for a two-sided hypothesis test to determine if there is a significant difference in the proportion of transactions completed within 5 minutes with the new POS system?

BlackTom AI · Accepted Answer

We start by restating what the question asks: how to use R's prop.test() to test whether there is a significant difference in the proportion of transactions completed within 5 minutes after adopting a new POS system, given x = 150 successes out of n = 200 trials, and a null proportion p0 = 0.80, with a two-sided alternative.

Option analysis:
Option: prop.test(150, 200, 0.80, alt = "two.sided", correct = FALSE)
- First issue: prop.test uses the argument name alternative for specifying the alternative hypothesis. Here, the option uses alt = "two.sided", which is not a recognized parameter name for prop.test in R. This means R will throw an error or ignore the intended setting, depending on the exact call environment.
- Second issue: The expression includes correct = FALSE. The prop.test function does not have a parameter named correct. This parameter name is associated with a different test (for example, certain binomial tests or specific tests with continuity corrections), but it is not valid for prop.test. Including an invalid argument name can cause an error or be ignored, but it indicates a misunderstanding of the function's arguments.
- Third issue: The third positional argument 0.80 corresponds to the null probability p under H0, which is appropriate, and matches the intent, provided the rest of the arguments were specified correctly.
- Fourth issue: Even if we fixed the argument names, using two.sided is the correct choice for a two-sided test, so that part is conceptually correct; the primary problems are the incorrect argument names and the extraneous correct parameter.

A correct usage would look like one of the following forms:
- prop.test(150, 200, p = 0.80, alternative = "two.sided")
- prop.test(x = 150, n = 200, p = 0.80, alternative = "two.sided")
- Or, equivalently, prop.test(150, 200, p = 0.80, alternative = "two.sided") if positional arguments are used, ensuring the parameter names align with R's function signature.

In summary, the given option is incorrect because it uses an unrecognized argument name (alt) and an invalid argument (correct). The correct approach requires naming the alternative as alternative and not introducing any non-existent parameters; and ensuring the null proportion p is specified with p = 0.80. The essential components—x = 150, n = 200, p = 0.80, and alternative = "two.sided"—are present in the intended correct form, while the extra incorrect argument names invalidate the call.

DATA1001/1901 (ND) Evaluate Quiz 9

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