Refer to the Development Psychology (Mar. 2003) study of the behavior of elementary school children. The researchers used a quadratic equation to model the level (y) of aggressive fantasies experienced by a child as. a function of the child's age (x). [Note: Level y was measured as an average of responses to six questions (e.g., "Do you sometimes have daydreams about hitting or hurting someone you don't like?"). Responses were measured on a scale ranging from 1 (never) to 5 (always).] a. Write the equation of the hypothesized model for E(y). b. Research psychologists theorized that a child's aggressive fantasies increase with age but at a slower rate of acceleration in older children. Sketch the curve hypothesized by the researchers. c. Set up $H_0$ and $H_a$ for testing the researchers' theory. d. The model was fitted to data collected for over 11,000 elementary school children, with the following results: $\hat{y}=1.926+.097 x-.003 x^{2}$, standard error of $\hat{\beta}_{2}=.001$. Compute the test statistic for the test you set up in part c. e. Use the result you found in part d to make the appropriate conclusion. Take $\alpha=.05$.

Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviations from the nominal surface smoothness in coded units. The joint probability distribution of the two measurements is a uniform distribution over the region 0 < x < 4, 0 < y, and x - 1 < y < x + 1. That is, $f_{X Y}(x, y)=c$ for x and y in the region. Determine the following: (a) P(X < 0.5, Y < 0.5) (b) P(X < 0.5) (c) E(X) (d) E(Y)

Find a nonhalting Turing machine that begins with a single 1 on its tape and successively generates strings of the form $0^{n} 10^{n}, n \geq 1,$ that is, such strings appear every so often on the tape.

The impulse J due to a force F is the product of the force times the amount of time t for which the force acts. When the force varies over time, $J=\int_{t_{1}}^{t_{2}} F(t) d t$. We can model the force acting on a rocket during launch by an exponential function $F(t)=A e^{b t}$, where A and b are constants that depend on the characteristics of the engine. At the instant lift-oft occurs (t=0), the force must equal the weight of the rocket. (a) Suppose the rocket weighs 25,000 N (a mass of about 2500 kg or a weight of 5500 lb), and 30 seconds after lift-off the force acting on the rocket equals twice the weight of the rocket. Find A and b. (b) Find the impulse delivered to the rocket during the first 30 seconds after the launch.

Find parametric equations for the following curve. Include an interval for the parameter values. Answer is not unique. A circle centered at the origin with radius 4, generated counterclockwise

Divide. $\left(40 h-8 h^{3}\right) \div(8 h)$

According to Freud infants become attached to the person or object that __________________________.

Piaget suggests that a child who encounters an experience that does not quite fit an existing schema will have to modify that schema somewhat. He called this process:

A) accommodation.

B) internalization.

C) assimilation.

D) operationalizing.

Define accommodation. What does accommodation accomplish?

A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal in order for 99% of the products to exceed 10,000 hours before failure?

Construct a (7, 3) code in which every nonzero codeword has Hamming weight at least 4.

Find the indefinite integrals. $\int\left(\frac{x}{7}-\frac{3}{4} x^{4}\right) d x$

Find an equation of the least squares linear regression line of y and x for the given data, and sketch both the line and the data. Predict the value of y corresponding to x=3.5.

$$\begin{array}{ccccccc} x & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline y & 1 & 1.8 & 2 & 4 & 4.5 & 7 & 9 \end{array}$$

Humans and warm-blooded animals maintain a constant body temperature, which is typically higher than their environment. (a) Estimate the maximum efficiency of a thermodynamic engine that is powered by this temperature difference in moderate climate conditions (the living organism is the hot reservoir and the environment is the cold reservoir). (b) Determine the output power of such an engine if the rate at which the energy is transferred from the living organisms to the engine is 100 W.