Third try and I still do not quite understand this problem (despite the wonderful explanation). I am so sorry, but I truly need help and I don't know the answers. Help from anyone would be amazing! :)

Question

6.42 Evolution versus Creationism:  A Gallup Poll released in December 2010 asked 1019 adults living in the Continental U.S. about their belief in the origin of humans. These results, along with results from a more comprehensive poll from 2001 (that we will assume to be exactly accurate - i.e. known values), are summarized in the table below:

ResponseYear: 2010Year: 2001
Humans Evolved with God guiding (1)	38%	37%
Humans evolved but God had no part in the process (2)	16%	12%
God created humans in present form (3)	40%	45%
Other / No opinion (4)	6%	6%

*** The second column above is "Year: 2010" and the third column is "Year: 2001" ***

(a) State hypotheses for the following research question: have beliefs on the origin of human life changed since 2001?

a. Ho: the population follows the 2001 distribution

Ha: the population doesn't follow the 2001 distribution

b. Ho: the population follows the 2010 distribution

Ha: the population doesn't follow the 2010 distribution

c. Ho: the population follows the 2001 distribution

Ha: the population follows the 2010 distribution

(b/c) Calculate the actual number of respondents in 2010 that fall in each response category (round to the nearest integer). Also calculate the expected number, assuming that the population follows the 2001 distribution (keep one decimal place).

ResponseObserved 2010Expected 2010
Humans Evolved with God guiding (1)
Humans evolved but God had no part in the process (2)
God created humans in present form (3)
Other / No opinion (4)

*** The second column above is "Observed 2010" and the third column is "Observed 2010" ***

(d) Conduct a chi-square test and state your conclusion.

The value of the test statistic is: __________ (please round to two decimal places) 

The degrees of freedom for this test are: __________

The p-value for this test is: __________ (please round to four decimal places) 

State the conclusion of the test in the context of the problem: __________

a. The data provide sufficient evidence to claim that the 2010 distribution is different than the distribution in 2001

b. The data to not provide sufficient evidence to claim that the 2010 distribution is different than the distribution in 2001

I am begging for anyone to help me with the answers to all blanks and multiple choice questions. The help provided with the question confused me and was somewhat insufficient.

Answer 1

We are trying to see if the 2010 values are different from the 2001 values when we know the true 2001 values and have a sample of the 2010 values.

Thus, the first choice in a is the solution; we are testing if the 2010 value is significantly different from the 2001 values.

b - c We get the value in all 8 cells of the table by multiplying the percentages in the top table by 1019, the sample size from the 2010 study.

Values in column 2 are 387.22; 163.04; 407.6; 61.14

Values in column 3 are 377.03; 122.28; 458.55; 61.14;

d The value of the test statistic is calculated by, in each row of the b-c table, calculating (actual - expected)^2/expected, and adding these 4 values. For example, from the first row, we get (387.22 - 377.03)^2/377.03 = .2754 (values are calculated from exact values).

The values are 0.28; 13.59; 5.66; 0

The sum is 19.52

Since we have 4 groups, df = g - 1 = 3

If we use the rounded 19.52, the p-value is, from Excel, =CHISQ.DIST.RT(19.52,3) = .0002

When not stated, one assumes that α =.05

p < α, so we reject the null hypothesis that the 2010 population follow the 2001 distribution.

a is the answer.