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Problem:

Problem:. If I have a group of 100 applicants for a college summer program whose mean SAT-Verbal is 525, is this group of applicants “above national average ”?. Problem:.

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Problem:

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  1. Problem: • If I have a group of 100 applicants for a college summer program whose mean SAT-Verbal is 525, is this group of applicants “above national average”?

  2. Problem: • If I have a group of 100 applicants for a college summer program whose mean SAT-Verbal is 525, is this group of applicants “above national average”? • Can I come up with a confidence interval for the “true value” of the population from which this group of applicants was drawn?

  3. GOSSET, William Sealy 1876-1937

  4. GOSSET, William Sealy 1876-1937

  5. GOSSET, William Sealy 1876-1937

  6. The t-distribution is a family of distributions varying by degrees of freedom (d.f., where d.f.=n-1). At d.f. =, but at smaller than that, the tails are fatter.

  7. X -  X -  _ _ z = t = - - X sX s - sX =  N

  8. The t-distribution is a family of distributions varying by degrees of freedom (d.f., where d.f.=n-1). At d.f. =, but at smaller than that, the tails are fatter.

  9. Degrees of Freedom df = N - 1

  10. Problem Sample: Mean = 54.2 SD = 2.4 N = 16 Do you think that this sample could have been drawn from a population with  = 50?

  11. X -  t = - sX Problem Sample: Mean = 54.2 SD = 2.4 N = 16 Do you think that this sample could have been drawn from a population with  = 50? _

  12. The mean for the sample of 54.2 (sd = 2.4) was significantly different from a hypothesized population mean of 50, t(15) = 7.0, p < .001.

  13. The mean for the sample of 54.2 (sd = 2.4) was significantlyreliably different from a hypothesized population mean of 50, t(15) = 7.0, p < .001.

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