Question

Researchers at Carnegie Mellon University have supposedly found that people find sandwiches tastier if they were made by someone else, rather than if they make the sandwiches themselves (2013). A researcher at SDSU decides to replicate the study to investigate whether people really do find sandwiches tastier if the sandwich maker is someone else versus themselves. The researcher learns that the average tastiness rating of self-made sandwiches in the population is µ= 3.4 on a 6-point scale (higher scores indicate greater tastiness), with a standard deviation of σ = 0.53. The researcher enlists his assistant, Mr. Pickles, and instructs him to make a large quantity of a basic sandwich. The researcher obtains a sample of 48 SDSU students and asks them to each eat one of the sandwiches made by Mr. Pickles and rate the tastiness of the sandwich using the same 6-point scale. The average rating of tastiness of the sandwich was M = 3.6. Use α = .05 for this significance test. Step 2: Assume that we draw all possible random samples of 48 people from the population of all adults. What would be the appropriate standard error (SE) for a distribution of samples of size 48? Give an interpretation in words of what this number means.

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Answer to a math question Researchers at Carnegie Mellon University have supposedly found that people find sandwiches tastier if they were made by someone else, rather than if they make the sandwiches themselves (2013). A researcher at SDSU decides to replicate the study to investigate whether people really do find sandwiches tastier if the sandwich maker is someone else versus themselves. The researcher learns that the average tastiness rating of self-made sandwiches in the population is µ= 3.4 on a 6-point scale (higher scores indicate greater tastiness), with a standard deviation of σ = 0.53. The researcher enlists his assistant, Mr. Pickles, and instructs him to make a large quantity of a basic sandwich. The researcher obtains a sample of 48 SDSU students and asks them to each eat one of the sandwiches made by Mr. Pickles and rate the tastiness of the sandwich using the same 6-point scale. The average rating of tastiness of the sandwich was M = 3.6. Use α = .05 for this significance test. Step 2: Assume that we draw all possible random samples of 48 people from the population of all adults. What would be the appropriate standard error (SE) for a distribution of samples of size 48? Give an interpretation in words of what this number means.

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Seamus
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The standard error measures how much variability or "standard" error there is from one sample mean to another if you took many samples from the population. It gives us an idea of how much the sample mean M is expected to vary because of random sampling error. A smaller SE indicates that the sample mean is likely to be closer to the population mean. The standard error (SE) for a distribution of sample means with a size of 48 is approximately 0.0765. In terms of interpretation, this number means that if we were to draw many samples of 48 people each from the population and calculate the mean tastiness rating for each sample, we would expect the distribution of those sample means to have a standard deviation of approximately 0.0765. This reflects the average amount that a sample mean would differ from the true population mean due to random chance when using samples of this size.

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