Problem 1
Classify each as independent or dependent samples. a. Heights of identical twins b. Test scores of the same students in English and psycholog 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
When one is computing the \(F\) test value, what condition is placed on the variance that is in the numerator?
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 2
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. Retention Test Scores A random sample of nonEnglish majors at a selected college was used in a study to see if the student retained more from reading a 19 th-century novel or by watching it in DVD form. Each student was assigned one novel to read and a different one to watch, and then they were given a 100 -point written quiz on each novel. The test results are shown. At \(\alpha=0.05,\) can it be concluded that the book scores are higher than the DVD scores? $$ \begin{array}{l|lllllll} \text { Book } & 90 & 80 & 90 & 75 & 80 & 90 & 84 \\ \hline \text { DVD } & 85 & 72 & 80 & 80 & 70 & 75 & 80 \end{array} $$
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
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. Improving Study Habits As an aid for improving students’ study habits, nine students were randomly selected to attend a seminar on the importance of education in life. The table shows the number of hours each student studied per week before and after the seminar. At \(\alpha=0.10\), did attending the seminar increase the number of hours the students studied per week? $$ \begin{array}{l|rrrrrrrrr} \text { Before } & 9 & 12 & 6 & 15 & 3 & 18 & 10 & 13 & 7 \\ \hline \text { After } & 9 & 17 & 9 & 20 & 2 & 21 & 15 & 22 & 6 \end{array} $$
Problem 3
The mean noise level of 20 randomly selected areas designated as "casualty doors" was \(63.1 \mathrm{dBA},\) and the sample standard deviation is \(4.1 \mathrm{dBA}\). The mean noise level for 24 randomly selected areas designated as operating theaters was \(56.3 \mathrm{dBA}\), and the sample standard deviation was \(7.5 \mathrm{dBA}\). At \(\alpha=0.05,\) can it be concluded that there is a difference in the means?
Problem 3
What are the two different degrees of freedom associated with the \(F\) 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. \(\hat{p}=0.35, n=200\)
