We have specified the "tailedness" of a hypothesis test for a population mean with null hypothesis $H_{0}: \mu=\mu_{0}$. For each exercise. a. draw the ideal power curve. b. explain what your curve in part (a) portrays. two-tailed

The following pseudocode describes how to obtain the name of a day, given the day number (0= Sunday, 1=Monday, and so on. ) Define a string called names containing "SunMonTueWedThufrisat".Compute the starting position as 3x the day number.Extract the substring of names at the starting position with length 3.Check this pseudocode, using the day number 4 . Draw a diagram of the string that is being computed.

Show that

$$\frac { P ( H | E ) } { P ( G | E ) } = \frac { P ( H ) } { P ( G ) } \frac { P ( E | H ) } { P ( E | G ) }$$

Suppose that, before new evidence is observed, the hypothesis H is three times as likely to be true as is the hypothesis G. If the new evidence is twice as likely when G is true than it is when H is true, which hypothesis is more likely after the evidence has been observed?

Identify the hypothesis and conclusion of the conditional statement.

If x + 8 = 4, then x = -4.

Underline the hypothesis and circle the conclusion. If a polygon is a pentagon, then it has five sides.

Tell whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply. $(-3,1),(-1,3),(1,1)$, and $(-1,-1)$

Merck & Co. conducted a study to test the promise of its experimental AIDS vaccine (The Boston Globe, September 22, 2007). Volunteers in the study were all free of the human immunodeficiency virus (HIN), which causes AIDS, at the start of the study, but all were at high risk for getting the virus. Volunteers were given either the vaccine or a dummy shot; 24 of 741 volunteers who got the vaccine became infected with $\mathrm{HIN}$, whereas 21 of 762 volunteers who got the dummy shot became infected with $\mathrm{HIV}$. The following table summarizes the results of the study.

$$\begin{array}{|l|c|c|} \hline & \text { Vaccinated } & \text { Dummy Shot } \\ \hline \text { Infected } & 24 & 21 \\ \hline \text { Not Infected } & 717 & 741 \\ \hline \end{array}$$

b. What is the probability that a randomly selected volunteer got vaccinated?

Identify the hypothesis and conclusion of the conditional. The dog will bark if a stranger walks by the house.

Indicate whether the following statements are true or false. Explain. Even very small amounts of oxides of nitrogen in the exhaust of an internal combustion engine can be a source of air pollution.

A particle carrying charge $q _ { \mathrm { p } } = + 10 \mathrm { nC }$ is located at $y _ { p } = 0.030 \mathrm { m }$ on the y axis of an xy coordinate system. A nonconducting rod of length $\ell = 0.10 \mathrm { m }$ carrying charge $q _ { \mathrm { r } } = - 10 \mathrm { nC }$ lies on the x axis, extending from x = 0 to x = 0.10 m. Write an expression for the electrostatic potential for any position along the y axis.

We have specified the "tailedness" of a hypothesis test for a population mean with null hypothesis $H_{0}: \mu=\mu_{0}$. For each exercise. a. draw the ideal power curve. b. explain what your curve in part (a) portrays. left-tailed

Recognize the hypothesis and conclusion of the statement. If $34-3 x=16$, then $x=6$.

Of the volunteers donating blood in a clinic, 80% have the Rhesus (Rh) factor present in their blood. What is the smallest number of volunteers who must be selected if we want to be at least 90% certain that we obtain at least five donors with the Rh factor?

During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V(x)$, where

$$V(x)=2 x^2-32 x+150$$

between the months of January and August. Here $x$ is time in months, with $x=1$ representing January. From August to December, $V(x)$ is modeled by

$$V(x)=31 x-226 .$$

Find the number of volunteers in each of the following months.

August