Question #1: On April 5, 2022, the Dox Research Center released the findings of an international poll on climate change

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Question #1: On April 5, 2022, the Dox
Research Center released the findings of an international poll on
climate change. The researchers polled residents of 40 countries on
a number of different issues, including whether they believed that
climate change (global warming) was currently harming people around
the world. The table below provides the question that was asked
along with the percentages of individuals in China and the United
States who indicated that climate change was currently causing
harm.
Do you believe that climate change is harming people
around the world now?
China
United States
Harming
52%
46%
Not Harming
48%
54%
The international poll included 750 people from China and 900
people from the United States. The margin of error was ±3.5
points for China and ±3.0 points for the United States.
Perform a goodness-of-fit test (i.e., a one-sample chi-square
test) to determine whether the general public in
China is more or less inclined to view global
warming as currently causing global harm. Note
that for this and subsequent tests you must change the numbers in
the table from percentages to frequencies.
(a) From the table it appears that a
majority of Chinese views climate change as currently harming
people around the world. Why then is a goodness-of-fit test
necessary to determine that this majority exists? What more will
the test tell us?
(b) Set up your null and alternative
hypotheses for the goodness-of-fit test. State these
hypotheses in words and mathematically.
(c) What is your decision rule for this
test? Make sure that you indicate the number of degrees of
freedom involved here.
(d) Calculate the appropriate inferential
statistic. Make sure that you indicate the numbers that you plug
into your formulas.
(e) Do a second test to see whether the
general public in the United
States is more or less inclined to view climate
change as currently harming people. You do not have to restate your
hypotheses and decision rule here as these will be essentially the
same as above. However, do calculate the appropriate test
statistic.
Perform a test of independence (i.e., a two sample chi-square
test) to determine whether the general public in China or the
United States is more likely to view climate change as currently
harming people.
(f) What are your null and alternative
hypotheses here? State these hypotheses in words as well as
mathematically.
(g) What is your decision rule?
Remember to indicate the degrees of freedom for this
test.
(h) Calculate the appropriate inferential
statistic. Again, remember to show all of the numbers that you plug
into the formulas that you use.
(i) Reviewing the results for your three
statistical tests, what can you say about the public’s views of
climate change in China and the United States? In short, what
decisions did you make for eachof
your three tests, and what conclusions did you reach based
on each test? Summarize
your results overall.