A recent study of perfect pitch tested students in American music conservatories. It found that 7% of 1700 non-Asian and 32% of 1000 Asian students have perfect pitch. A test of the difference in proportions resulted in a P-value of < 0.0001. a) What are the researchers’ null and alternative hypotheses? b) State your conclusion. c) Explain in this context what the P-value means. d) The researchers claimed that the data prove that genetic differences between the two populations cause a difference in the frequency of occurrence of perfect pitch. Do you agree? Why or why not?

An object moving back and forth along a straight line is said to undergo vibrational motion if its displacement from equilibrium at time t is given by an equation of the form $x(t)=e^{-k t}(A \cos \omega t+B \sin \omega t)$ where A, B, k, and $\omega$ are constants. Answer the following questions about the given function x(t) with this form for the indicated time interval $a \leq x \leq b:$ (a) Sketch the graph of x(t). You may wish to use the graphing utility on your calculator. (b) Find the values of t for which the largest and smallest values of x(t) occur for $a \leq t \leq b. \quad x(t)=e^{-t}(\sin t+\cos t)$ for $\frac{\pi}{2} \leq t \leq \frac{3 \pi}{2}$

For each pair of propositions P and Q, state whether or not P$\equiv$Q P=$p\rightarrow q$ Q=$\neg p\vee q$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$$\left\{\begin{array}{l}{3 x+3 y=-1} \\ {4 x+y=\frac{8}{3}}\end{array}\right.$$

Game wardens have determined that the maximum wolf population in a certain preserve is 1000 wolves. Suppose the population of wolves in the preserve in the year 2000 was 500, and that k is estimated to be 0.025. a. Find a logistic function for the number of wolves in the preserve in year t, where t is the number of years after 2000. b. Find the estimated wolf population in 2025.

Calculate the efficiency of the circuit of $V_{CC}=36\;\mathrm{V}$ and $P_{o}=2\;\mathrm{W}$ if the bias current is $I_{C_{Q}}=150\;\mathrm{mA}$.

$$\begin{matrix} \text{} & \text{X} & \text{Y} & \text{Z} & \text{Totals}\\ \text{S} & \text{.10} & \text{.25} & \text{.15} & \text{.50}\\ \text{T} & \text{.05} & \text{.20} & \text{.02} & \text{.27}\\ \text{R} & \text{.05} & \text{.15} & \text{.03} & \text{.23}\\ \text{Totals} & \text{.20} & \text{.60} & \text{.20} & \text{1.00}\\ \end{matrix}$$

Find $P(R \cap Z)$.

Graph the solutions of each inequality on a number line. a<3

What can you say about two lines that have equal slopes and equal y-intercepts?

Solve equation $600a=2,400$

A bank offers annual rates of 4% simple interest or 3.5% compound interest on its savings accounts. Determine the length of time an account must be held for the two choices to be equally attractive. Round to the nearest tenth.

Medical literature says that about 8% of males are color-blind. A university's introductory psychology course is taught in a large lecture hall. Among the students, there are 325 males. Each semester when the professor discusses visual perception, he shows the class a test for color blindness. The percent age of males who are color blind varies from semester to semester

Is the sampling distribution model for the sample proportion likely to be Normal ? Explain.

It's estimated that 50,000 pregnant women worldwide die each year of eclampsia, a condition involving elevated blood pressure and seizures. A research team from 175 hospitals in 33 countries investigated the effectiveness of magnesium sulfate in preventing the occurrence of eclampsia in at-risk patients. Results are summarized below.

$$\begin{array}{|c|c|c|c|c|c|} \hline & & \begin{array}{l} \text { Reported } \\ \text { side effects } \end{array} & \begin{array}{l} \text { Developed } \\ \text { eclampsia } \end{array} & \text { Deaths } & \begin{array}{c} \text { Total } \\ \text { Subjects } \end{array} \\ \hline & \begin{array}{l} \text { Magnesium } \\ \text { sulfate } \\ \text { Placebo } \end{array} & \begin{array}{r} 1201 \\ 228 \end{array} & \begin{array}{l} 40 \\ 96 \end{array} & \begin{array}{l} 11 \\ 20 \end{array} & \begin{array}{l} 4999 \\ 4993 \end{array} \\ \hline \end{array}$$

a) Write a 95% confidence interval for the increase in the proportion of women who may develop side effects from this treatment. Interpret your interval.

b) Is there evidence that the treatment may be effective in preventing the development of eclampsia? Test an appropriate hypothesis and state your conclusion.

A cable hanging under its own weight has a slope $S=d y / d x$ that satisfies $d S / d x=c \sqrt{1+S^{2}}$. The constant c is the ratio of cable density to tension. Show that $S = \sinh(cx)$ satisfies this equation.