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: Response Year: 2010 Year: 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% (a) State hypotheses for the following research questions have beliefs on the origin of human life changed since 20012 O Ho: the population follows the 2001 distribution Ha: the population doesn't follow the 2001 distribution O Ho: the population follows the 2001 distribution Ha: the population follows the 2010 distribution O Ho: the population follows the 2010 distribution Ha: the population doesn't follow the 2010 distribution Ibic) 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). Response Observed 2010 Expected 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) d) Conduct a chi-square test and state your conclusion MacBook Pro CO 39 05C S 4 % 5 & 7 1 2 3 6 8 O Q W E T Y tab А S D F G HJ caps lock N х C V B N 92

Answer 1

ANSWER:

For the given data

Hypothesis:

a)

H₀: The population follows the 2001 distribution

Ha: The population doesn't follow the 2001 distribution

b /c)

Response	observed (O)	Expected(E)	(O-E)	(O-E)2/E
1	387	377	10	0.275405405
2	163	122	41	13.58666667
3	408	459	-51	5.661111111
4	61	61	0	0
total	1019	1019	0	20

d)

chi-square=sum((O-E)²/E) = 19.52 with k -1= 4 -1=3 df ( degree of freedom=3)

p-value=0.0002 ( using ms-excel =CHIDIST(19.52,3))

since level of significance is not mentioned here, let its typical value alpha=0.05,

since p-value is less than alpha=0.05, we fail to accept null hypothesis H₀

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

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