Two examples analyzed whether telephone callers to an airline would stay on hold different lengths of time, on average, if they heard

(a) an advertisement about the airline,

(b) Muzak, or

(c) classical music. The sample means were 5.4, 2.8, and 10.4, with $n_1$ = $n_2$ = $n_3$ = 5. The ANOVA test had F = 74.6/11.6 = 6.4 and a P-value of 0.013.

The 95% confidence intervals are (0.3, 9.7) for $\mu_3$ - $\mu_1$ and (-2 .1, 7.3) for $\mu_1$ - $\mu2$. Interpret these two confidence intervals. Using these two intervals and the interval from part a, summarize what the airline company learn ed from this study.

For the House Selling Prices GI) OR data file on the book 's website, the table shows the result of conducting an ANOVA comparing mean house selling prices (in $1000) by Age Category (New = 0 to 24 years old, Medium = 25 to 50 years old, Old = 51 to 74 years old, Very Old = 75 + years old). It also shows a summary table of means and standard deviations of the selling prices, by age group.

Interpret the confidence interval.

The Anorexia data file on the book's website shows weight change for anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a control treatment). Use software to analyze these data. (The change scores are in the last three columns of the data set. Alternatively, the website also contains a data set that shows the data in "long" format, with the treatment in one column and the change score in another column.)

State and check the assumptions for the test in part b.

For the House Selling Prices GI) OR data file on the book 's website, the table shows the result of conducting an ANOVA comparing mean house selling prices (in $1000) by Age Category (New = 0 to 24 years old, Medium = 25 to 50 years old, Old = 51 to 74 years old, Very Old = 75 + years old). It also shows a summary table of means and standard deviations of the selling prices, by age group.

Using information given in the tables, show how to construct a 95% confidence interval comparing the population means of new and medium-aged houses.

The Anorexia data file on the book's website shows weight change for anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a control treatment). Use software to analyze these data. (The change scores are in the last three columns of the data set. Alternatively, the website also contains a data set that shows the data in "long" format, with the treatment in one column and the change score in another column.)

For the one-way ANOVA comparing the three mean weight changes, report the test statistic and P-value. Explain how to interpret.

The Anorexia data file on the book's website shows weight change for anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a control treatment). Use software to analyze these data. (The change scores are in the last three columns of the data set. Alternatively, the website also contains a data set that shows the data in "long" format, with the treatment in one column and the change score in another column.)

Construct box plots for the three groups. Use these and sample summary means and standard deviations to describe the three samples.

The relativistic expression for kinetic energy should be used for the electron in the photoelectric effect when $v / c>0.1$, errors greater than about 1% are to be avoided. For photoelectrons ejected from an aluminum surface $\left(w_{0}=4.2 \mathrm{eV}\right)$ what is the smallest wavelength of an incident photon for which the classical expression may be used?

If one defines a variable mass $m_{\text {var }}=\gamma m$, the relativistic momentum $\gamma m \mathbf{u}$ becomes $m_{\mathrm{var}} \mathbf{u}$, which looks more like the classical definition. Show, however, that the relativistic kinetic energy $(\gamma-1) m c^2$ is not equal to $\frac{1}{2} m_{\mathrm{var}} u^2$.

Consider a free particle of mass m. Show that the position and momentum operators in the Heisenberg picture are given by

$$\begin{array}{l}{\hat{x}_{H}(t)=\hat{x}_{H}(0)+\frac{1}{m} \hat{p}_{H}(0) t} \\ {\hat{p}_{H}(t)=\hat{p}_{H}(0)}\end{array}$$

. Comment on the relationship between these equations and the classical equations of motion. Hint: you will first need to evaluate the commutator $\left[\hat{x}, \hat{H}^{n}\right]$; this will allow you to evaluate the commutator $[\hat{x}, \hat{U}]$.

Solve the given problems.

In the theory of relativity, when studying the kinetic (moving) energy of an object, the equation $K=\left[\left(1-\frac{v^2}{c^2}\right)^{-1 / 2}-1\right] m c^2$ is used. Here, for a given object, $K$ is the kinetic energy, $v$ is its velocity, and $c$ is the velocity of light. If $v$ is much smaller than $c$, show that $K=\frac{1}{2} m v^2$, which is the classical expression for $K$.

An electron moving initially at constant (nonrelativistic) speed v is brought to rest with uniform deceleration a lasting for a time t=v/a. Compare the electromagnetic energy radiated during the deceleration with the electron’s initial kinetic energy. Express the ratio in terms of two lengths, the distance light travels in time t and the classical electron radius $r_{0}$, defined as $e^{2} / 4 \pi \epsilon_{0} m c^{2}$.

Use the classical adjoint formula to,compute the inverses of each of the following $3 \times 3$ real matrices.

$$\left[\begin{array}{rrr}{-2} & {3} & {2} \\ {6} & {0} & {3} \\ {4} & {1} & {-1}\end{array}\right], \quad\left[\begin{array}{ccc}{\cos \theta} & {0} & {-\sin \theta} \\ {0} & {1} & {0} \\ {\sin \theta} & {0} & {\cos \theta}\end{array}\right]$$

Today we label people as heroes to acknowledge their bravery or hard work. To the writer of classical tragedies, however, a hero was a more complex character. A hero was a strong, often admirable person who failed to live up to his or her promise because of a tragic flaw. This might be a negative trait or a positive one that is inflexible or taken to excess.

Reread Teiresias's warning to Creon (Scene 5, lines 10-40). What flaw does the prophet specifically identify in the king's character? Do you believe that this weakness is sufficient to cause the tragedy that results? Explain.

In this proplem, you will estimate the classical lifetime of the hydrogen atom. An accelerating charge loses electromagnetic energy at a rate given by $\mathscr{P}=$ $-2 k_e q^2 a^2 /\left(3 c^3\right)$, where $k_e$ is the Coulomb constant, $q$ is the charge of the particle, $a$ is its acceleration, and $c$ is the speed of light in a vacuum. Assume that the electron is one Bohr radius $(0.0529 \mathrm{~nm})$ from the center of the hydrogen atom. (a) Determine its acceleration