Imagine that a researcher conducts a two-tailed z test with an alpha level of 0.05 (i. e., 5%). The researcher expects to find that the population that she samples from will differ from her comparison population. What sets of answers would constitute appropriate null and alternative hypotheses for this study?

Null hypothesis :

Alternative hypothesis:

Or equivalently:

Null hypothesis :

Alternative hypothesis:

Other important thing is that on the alternative hypothesis we never can have the symbol equal.  

Step-by-step explanation:

Some previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

On this case the she wants to proof if that she samples from will differ from her comparison population. So this needs to be on the alternative hypothesis. And the complement of the alternative hypothesis would be on the null hypothesis.  

Solution to the problem

So then she needs to conduct a two tailed z test. Let's assume that the population 1 is the population of interest and the population 2 is the comparison population so then the systam of hypothesis are:

Null hypothesis :

Alternative hypothesis:

Or equivalently:

Null hypothesis :

Alternative hypothesis:

Other important thing is that on the alternative hypothesis we never can have the symbol equal.  

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%