State in detail under what conditions it is possible to make a causal inference from a comparison of means between two or more groups of individuals.

Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?

In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference

The time a patient must wait before being attended by a physician in a hospital has been observed for each of 100 randomly selected patients he sample mean is 70.3 minutes and the standard deviation is 28.2 minutes. Test the hypothesis that the mean waiting time in the hospital is not more than 65 minutes.

Give a correct answer for the difference between internal and external validity is best described as:

Water flows through a water hose at a rate of ${\displaystyle Q_1=680c\frac{m^3}{s}}$, the diameter of the hose is ${\displaystyle d_1=2.2cm}$. A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of ${\displaystyle v_2=9.2\frac{m}{s}}$.
a) Enter an expression for the cross-sectional area of the hose, ${\displaystyle A_1}$, in terms of its diameter, ${\displaystyle d_1}$
b) Calculate the numerical value of ${\displaystyle A_1,}$ in square centimeters.
c) Enter an expression for the speed of the water in the hose, ${\displaystyle v_1}$, in terms of the volume floe rate ${\displaystyle Q_1}$ and cross-sectional area ${\displaystyle A_1}$
d) Calculate the speed of the water in the hose, ${\displaystyle v_1}$ in meters per second.
e) Enter an expression for the cross-sectional area of the nozzle, ${\displaystyle A_2}$, in terms of ${\displaystyle v_1,v_2}$ and ${\displaystyle A_1}$
f) Calculate the cross-sectional area of the nozzle, ${\displaystyle A_2}$ in square centimeters.

Iron is very important for babies' growth. A common belief is that breastfeeding will help the baby to get more iron than formula feeding. To justify the belief, a study followed 2 groups of babies from born to 6 months. With one group babies are breast fed, and the other group are formula fed without iron supplements. Data below shows iron levels of those two groups of babies.

$\begin{array}{|cccc|}\hline Group& Samplesize& mean& Standarddeviation\\ Breast-fed& 23& 13.3& 1.7\\ Formula-fed& 23& 12.4& 1.8\\ DIFF=Breast-Formula& 23& 0.9& 1.4\\ \hline\end{array}$

(1) There are two groups we need to compare for the study: Breast-Fed and Formula- Fed. Are those two groups dependent or independent? Based on your answer, what inference procedure should we apply for this research?

(2) Please perform the inference you decided in (1), and make sure to follow the 5-step procedure for any hypothesis test.

(3) Based on your conclusion in (2), what kind of error could you make? Explain the type of error using the context words for this research

In general, the t test for correlated groups is a more powerful test than the sign test. Is this statement true? Explain why? Can you think of situations in which the sign test might be more powerful than the t test for correlated groups (assume N is the same for both tests, etc.)?