Apolitician claims that a larger proportion of members of the news media are democrats when compared to the general public. let p1 represent the proportion of the news media that is democrat and p2 represent the proportion of the public that is democrat. what are the appropriate null and alternative hypotheses that correspond to this claim? h0: p1 - p2 = 0; ha: p1 - p2 < 0 h0: p1 - p2 = 0; ha: p1 - p2 > 0 h0: p1 - p2 = 0; ha: p1 - p2 ≠ 0

Null hypothesis: ,

Alternative hypothesis:  

Step-by-step explanation:

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".

Solution to the problem

Some Notation

represent the proportion of the news media that is Democrat

represent the proportion of the public that is Democrat

On this case the claim that they want to test is: "That a larger proportion of members of the news media are Democrats when compared to the general public". So we want to check if the population proportion p1 is higher than p2, so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Null hypothesis:

Or

The null hypothesis can be on this way: , but is better put the complement of the alternative hypothesis.    

Alternative hypothesis:  

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.