The t-statistic can be used to calculate p-value associated with the null
hypothesis. A small p-value is evidence that the null hypothesis is
correct. (5%)
The sample correlation coefficients is an estimator of the population
correlation coefficient and measure the linear relationship between two
variables, that is, how well their scatterplot is approximated by a
straight line. (5%)
A confidence interval contains less information than the result of a
single hypothesis test. (5%)
With small samples and large σ , quite large differences may not be
statistically significant but may be real and of great practical
significance. (5%)
An examination of sample items from a shipment showed that 51% of the
items were good and 49% were defective. The company president asked the
statistician, “What is the probability that over half the items are good?”
The statistician replied that the question cannot be answered from the
data. Is this correct? Does the question make sense? Explain why? (5%)
(a) What is the law of large numbers? Give two examples to illustrate the
use of the law of large numbers. (10%)
(b) What is the central limit theorem. Give two examples to illustrate the
use of central limit theorem. (10%)
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