The pita‑franchise owner has observed in the past that waiting times tend to have a long tail to the right, with most customers served relatively quickly and a few rare customers required to wait a very long time. Is a two‑sample t ‑test appropriate in this setting? The two‑sample t ‑test is appropriate because this is a comparison of the means of two continuous, random variables. The two‑sample t ‑test is not appropriate because the two samples do not have the same size. The two‑sample t ‑test is not appropriate because the sample standard deviations are not equal. The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small. The two‑sample t ‑test is appropriate because the samples are random and contain no outliers, and the populations are normal.

Question

Tobias Patton

Mathematics

12 September, 00:37

The pita‑franchise owner has observed in the past that waiting times tend to have a long tail to the right, with most customers served relatively quickly and a few rare customers required to wait a very long time. Is a two‑sample t ‑test appropriate in this setting? The two‑sample t ‑test is appropriate because this is a comparison of the means of two continuous, random variables. The two‑sample t ‑test is not appropriate because the two samples do not have the same size. The two‑sample t ‑test is not appropriate because the sample standard deviations are not equal. The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small. The two‑sample t ‑test is appropriate because the samples are random and contain no outliers, and the populations are normal.

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Solomon Barrett · Answer 1

The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small.

Step-by-step explanation:

The complete question is:

The owner of a pita franchise with two locations is interested in the average time that customers spend waiting for service at each store. She believes that the average waiting time at the original location is higher than the average waiting time at the new location.

The pita‑franchise owner has observed in the past that waiting times tend to have a long tail to the right, with most customers served relatively quickly and a few rare customers required to wait a very long time. Is a two‑sample t ‑test appropriate in this setting? The two‑sample t ‑test is appropriate because this is a comparison of the means of two continuous, random variables. The two‑sample t ‑test is not appropriate because the two samples do not have the same size. The two‑sample t ‑test is not appropriate because the sample standard deviations are not equal. The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small. The two‑sample t ‑test is appropriate because the samples are random and contain no outliers, and the populations are normal.

For two sample t-test the distributions must be normal. Here the data, as mentioned in the questions is skewed to the right with long waiting times in the past.