How important is the assumption The sampled population is normally distributed to the use of Student's t-distribution?
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a. Does the distribution appear to be normal? Find percentages for intervals and compare them with the normal distribution.
b. Does the distribution of t_ appear to have a t-distribution with df = 9? Find percentages for intervals and compare them with the t-distribution. For the samples from the rectangular or uniform population:
c. Does the distribution appear to be normal? Find percentages for intervals and compare them with the normal distribution.
d. Does the distribution of t_ appear to have a t-distribution with df = 9? Find percentages for intervals and compare them with the t-distribution. For the samples from the skewed (exponential) population:
e. Does the distribution appear to be normal? Find percentages for intervals and compare them with the normal distribution.
f. Does the distribution of t_ appear to have a t-distribution with df = 9? Find percentages for intervals and compare them with the t-distribution. In summary:
g. In each of the preceding three situations, the sampling distribution for appears to be slightly different from the distribution of t_. Explain why.
h. Does the normality condition appear to be necessary in order for the calculated test statistic t_ to have a Student's t-distribution? Explain
Distribution
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