Chapter 9: Problem 480
Find the midrange of this sample of SAT-Verbal scores. The sample had the smallest observation of 426 and the largest at 740 .
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Two independent reports on the value of a tincture for treating a disease in camels were available. The first report made on a small pilot series showed the new tincture to be probably superior to the old treatment with a Yates' \(\mathrm{X}^{2}\) of \(3.84, \mathrm{df}=1, \alpha=.05 .\) The second report with a larger trial gave a "not significant" result with a Yates \(\mathrm{X}^{2}=2.71, \mathrm{df}=1\), \(\alpha=.10 .\) Can the results of the 2 reports be combined to form a new conclusion?
Consider the joint distribution of \(\mathrm{X}\) and \(\mathrm{Y}\) given in the form of a table below. The cell (i,j) corresponds to the joint probability that \(\mathrm{X}=\mathrm{i}, \mathrm{Y}=\mathrm{j}\), for \(\mathrm{i}=1,2,3, \mathrm{j}=1,2,3\) $$ \begin{array}{|c|c|c|c|} \hline \mathrm{Y}^{\mathrm{X}} & 1 & 2 & 3 \\ \hline 1 & 0 & 1 / 6 & 1 / 6 \\ \hline 2 & 1 / 6 & 0 & 1 / 6 \\ \hline 3 & 1 / 6 & 1 / 6 & 0 \\ \hline \end{array} $$ Check that this is a proper probability distribution. What is the marginal distribution of \(\mathrm{X} ?\) What is the marginal distribution of \(\mathrm{Y}\) ?
Consider the distribution defined by the following distribution function: $$ \mathrm{F}(\mathrm{x})=0 \quad \text { if } \quad \mathrm{x}<0 $$ and \(=1-\mathrm{pex}^{-\mathrm{x}} \quad\) if \(\quad \mathrm{x} \geq 0\) for \(0<\mathrm{p}<1\) This distribution is partly discrete and partly continuous. Find the moment generating function of \(\mathrm{X}\) and use it to find the mean and variance of \(\mathrm{X}\).
Barnard College is a private institution for women located in New York City. A random sample of 50 girls was taken. The sample mean of grade point averages was \(3.0\). At neighboring Columbia College a sample of 100 men had an average gpa of \(2.5\). Assume all sampling is normal and Barnard's standard deviation is \(.2\), while Columbia's is \(.5\). Place a \(99 \%\) confidence interval on \(\mu_{\text {Barnard }}-\mu_{\text {Columbin }}\)
Let \(\mathrm{U}\) be a chi-square random variable with \(\mathrm{m}\) degrees of freedom. Let \(\mathrm{V}\) be a chi-square random variable with \(\mathrm{n}\) degrees of freedom. Consider the quantity. \(\mathrm{X}=(\mathrm{U} / \mathrm{m}) /(\mathrm{V} / \mathrm{n})\), where \(\mathrm{U}\) and \(\mathrm{V}\) are independent. Using the change of variable technique, find the probability density of \(\mathrm{X}\).
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