# In a 2014 Pew Research survey of adults in the U.S., respondents were asked whether or not

## Question:

In a 2014 Pew Research survey of adults in the U.S., respondents were asked whether or not they believed in God or a universal spirit and how certain they were of their belief. The results are displayed in the table shown below.

Belief in God .................................................................................. %
Believe in God; absolutely certain ............................................. 63
Believe in God; fairly certain ....................................................... 20
Believe in God; not too/not at all certain .................................... 5
Believe in God; don’t know ........................................................... 1
Do not believe in God ................................................................... 9
Don’t know if they believe in God ................................................ 2

A researcher wants to find out if the distribution is the same for the members of a Lutheran church in Minneapolis. The researcher administers a survey questionnaire to a random sample of 100 adult church members and obtains the distribution shown below.

Belief in God .......................................................................... %
Believe in God; absolutely certain ..................................... 80
Believe in God; fairly certain ................................................ 6
Believe in God; not too/not at all certain ........................... 4
Believe in God; don’t know .................................................. 3
Do not believe in God ........................................................... 2
Don’t know if they believe in God ........................................ 5

Carry out a one-variable chi-square test on these data by following these steps:

1. Present the null hypothesis.

2. Present the alternative hypothesis.

3. Calculate df.

4. Using Table D in your textbook, identify the critical χ2 value for a significance level of .05.

5. Calculate obtained χ2.

6. Present a statistical decision.

7. Based on your results, what would you say about the distribution of beliefs in the Lutheran church that was surveyed as compared to the U.S. distribution?

Distribution
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