Question 1
Compare the sampling distributions of the normally distributed test statistic
z and the chi-square test statistic. Specifically, how do the sampling distributions differ in shape and range of values?
Question 2
A dowsing rod is a "Y" or "L" shaped instrument that some believe can find ground water. Many dowsers today use a pair of simple L-shaped metal rods. One rod is held in each hand, with the short arm of the L held upright, and the long arm pointing forward. When something is found, the rods cross over one another making an "X" over the found object. Skeptics of dowsing conducted an experiment to see if dowsing rods could find ground water. Five identical 3 foot by 3 foot plots of land were sectioned off and a container of water was buried in one of the plots. Below is a summary of the experiment results and the output for the goodness-of-fit test.
Of the following statements, which one is
not true about the chi-square statistic and p-value? Choose (d) if all statements are true.
◦ Under the assumption that the null is true, the p-value is the probability that the chi-square statistic will be as big as or bigger than the observed value.
◦ The larger the chi-square statistic, the smaller the p-value.
◦ On the chi-square distribution, the p-value is represented by the area under the curve to the right of the chi-square statistic.
◦ All of these statements are true.
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