In 2009 news organizations reported that 47% of U. S. adults favored providing a legal way for illegal immigrants already in the U. S. to become citizens. In 2010, the percentage with this opinion rose to 50%. Suppose that a current poll of 100 randomly selected U. S. adults shows this percentage is higher than 50% this year. A researcher conducts a hypothesis test with the data from the current poll. She finds that the increase this year is not statistically significant. What conclusion can we draw

The exercise tells us about a process that has been submitted to public opinion and has obtained different results in the population, with different variations regarding the legalization of immigrants in the United States. This time, a survey with 100 adults obtained at random is being tested. and it has a result, finding significant changes with respect to the first event, however we must conclude that the sample size is too small to detect a statistically significant increase, due to the value of people surveyed, to have a more impactful result there should be more people surveyed

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

step-by-step :