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A journal article was recently published about typing skills, and in this article, the results of a national typing test were reported. The authors of the article claim that the population of those considered to be "skilled" typists can type an average of 80 words per minute, with a standard deviation of 2.5 words per minutes. Mrs. Gonzalez teaches typing at a local high school and she is concerned that her students are not as skilled as they could be when it comes to typing. One semester, she compiles data from the n = 100 students who have taken her typing course, and she finds this sample types an average of 79 words per minute. If, as the journal article claims, skilled typists can type an average 80 words per minute, is it likely that Mrs. Gonzalez would have observed a sample mean of 79 words per minute from her sample of 100 students, if in fact these students are skilled typists? Why or why not?
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