Problem 1
Classify each as independent or dependent samples. a. Heights of identical twins b. Test scores of the same students in English and psychology c. The effectiveness of two different brands of aspirin on two different groups of people d. Effects of a drug on reaction time of two different groups of people, measured by a before-and-after test e. The effectiveness of two different diets on two different groups of individuals
Problem 1
Explain the difference between testing a single mean and testing the difference between two means.
Problem 1
For these exercises, perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified and assume the variances are unequal. Waterfall Heights Is there a significant difference at \(\alpha=0.10\) in the mean heights in feet of waterfalls in Europe and the ones in Asia? The data are shown. $$ \begin{array}{ccc|ccc}{} & {} & {\text { Europe }} & {} & {\text { Asia }} \\\ \hline 487 & {1246} & {1385} & {614} & {722} & {964} \\ {470} & {1312} & {984} & {1137} & {320} & {830} \\ {900} & {345} & {820} & {350} & {722} & {1904}\end{array} $$
Problem 1
Find the proportions \(\hat{p}\) and \(\hat{q}\) for each. a. \(n=52, X=32\) b. \(n=80, X=66\) c. \(n=36, X=12\) d. \(n=42, X=7\) e. \(n=160, X=50\)
Problem 1
When one is computing the \(F\) test value, what condition is placed on the variance that is in the numerator?
Problem 2
For these exercises, perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified and assume the variances are unequal. Tax-Exempt Properties A tax collector wishes to see if the mean values of the tax-exempt properties are different for two cities. The values of the tax- exempt properties for the two random samples are shown. The data are given in millions of dollars. At \(\alpha=0.05,\) is there enough evidence to support the tax collector's claim that the means are different? $$ \begin{array}{cccc|cccc}{} & {\text { City } \mathbf{A}} & {} & {} & {} & {\text { City } \mathbf{B}} & {} & {} \\ \hline 113 & {22} & {14} & {8} & {82} & {11} & {5} & {15} \\ {25} & {23} & {23} & {30} & {295} & {50} & {12} & {9} \\ {44} & {11} & {19} & {7} & {12} & {68} & {81} & {2} \\ {31} & {19} & {5} & {2} & {} & {20} & {16} & {4} & {5}\end{array} $$
Problem 2
Find \(\hat{p}\) and \(\hat{q}\) for each. a. \(n=36, X=20\) b. \(n=50, X=35\) c. \(n=64, X=16\) d. \(n=200, X=175\) e. \(n=148, X=16\)
Problem 2
When a researcher selects all possible pairs of samples from a population in order to find the difference between the means of each pair, what will be the shape of the distribution of the differences when the original distributions are normally distributed? What will be the mean of the distribution? What will be the standard deviation of the distribution?
Problem 3
Find each \(X,\) given \(\hat{p}\) a. \(\hat{p}=0.60, n=240\) b. \(\hat{p}=0.20, n=320\) c. \(\hat{p}=0.60, n=520\) d. \(\hat{p}=0.80, n=50\) e. \(\hat{p}=0.35, n=200\)
Problem 3
What are the two different degrees of freedom associated with the \(F\) distribution?
