Application Assignment 7
1.) What factor determines whether you should use a z-score or a t statistic for a Hypothesis test?
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Total number of the sample population (n), when n is equal to or less than 30 use t-test, when larger than 30 use z-test. Small samples are not entirely normal in distribution, thus the t-distribution is used.
2.) Several factors influence the value obtained for a t statistic. Some factors affect the numerator of the t statistic and others influence the size of the estimated standard error in the denominator. For each of the following, indicate whether the factor influences the numerator or denominator of the t statistic and determine whether the effect would be to increase the value of t (farther from zero) or decrease the value of t (closer to zero). In each case, assume that all other factors remain constant.
a. Increase the variability of the scores. Increase denominator, decrease the value of t.
b. Increase the number of scores in the sample. Decrease denominator, increase the value of t.
c. Increase the difference between the sample mean and the population mean. Increase numerator, increase value of t.
5.) A sample of n = 16 scores has a mean of M = 45 and SS = 960.
a. Calculate the sample standard deviation (s) and the estimated standard error
for the sample mean (SM).
s = sqrt of SS/n-1
s = sqrt of 64
s = 8
SE = s/sqrt of n
SE = 8/4
SE = 2
b. Describe what is measured by the standard deviation and what is measured by
the estimated standard error.
Standard deviation is the measure of variability of the scores from the mean. The estimated standard error measures the difference between the variation of the sample mean from the true population mean.
12.) Last fall, a sample of n = 25 freshmen was selected to participate in a new 4-hour
training program designed to improve study skills. To evaluate the effectiveness
of the new program, the sample was compared with the rest of the freshman class.
All freshmen must take the same English Language Skills course, and the mean
score on the final exam for the entire freshman class was u = 74. The students in
the new program had a mean score of M = 78 with SS = 2400.
a. On the basis of these data, can the college conclude that the students in the new program performed significantly better than the rest of the freshman class? Use a one-tailed test with a = .05.
t = .0407 (0.05 alpha)
t = 1.708 at df = 24
No, the college cannot conclude that the students in the new program performed better than the rest of the freshman class.
b. Can the college conclude that the students in the new program are significantly different from the rest of the freshman class? Use a two-tailed test with a = .05.
t = .40 (0.05 alpha)
t = 2.06 at df = 24
No, the college cannot conclude that the students in the new program are significantly better than the rest of the freshman class.