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Magazine Problem 1
What assumptions are made when Student's \(t\) -test is used to test a hypothesis concerning a population mean?
Problem 1
What assumptions are made about the populations from which random samples are drawn when the \(t\) distribution is used to make small-sample inferences about the difference in population means?
Problem 1
Why use paired observations to estimate the difference between two population means rather than estimation based on independent random samples selected from the two populations? Is a paired experiment always preferable? Explain.
Problem 1
Find the tabled value for \(a \chi^{2}\) variable based on \(n-1\) degrees of freedom with an area of a to its right. \(n=10, a=.05\)
Problem 1
Under what assumptions can the \(F\) distribution be used in making inferences about the ratio of the population variances?
Problem 2
Calculate the number of degrees of freedom for \(s^{2}\), the pooled estimator of \(\sigma^{2}\). $$ n_{1}=16, \quad n_{2}=8 $$
Problem 2
Calculate the number of degrees of freedom for a paired-difference test in Exercises \(2-4,\)with \(n_{1}=n_{2}=\) number of observations in each sample and \(n=\) number of pairs. $$n_{1}=n_{2}=8$$
Problem 2
Find the tabled value of \(t\left(t_{a}\right)\) corresponding to a right-tail area a and degrees of freedom given in Exercises 2-6. $$ a=.05, d f=20 $$
Problem 2
Use the information given in Exercises \(2-7\) to find the tabled value for an \(F\) variable based on \(n_{1}-\) I numerator degrees of freedom, \(n_{2}-1\) denominator degrees of freedom with an area of a to its right. \(n_{1}=3, n_{2}=8, a=.050\)
Problem 2
Find the tabled value for \(a \chi^{2}\) variable based on \(n-1\) degrees of freedom with an area of a to its right. \(n=25, a=.95\)
