Question: The question about the importance of religion in Example was asked in a survey of elementary statistics students at Penn
State University from 2007 to 2010. The results were as follows:
Very important: 730 = 21.4%
Fairly important: 1512 = 44.3%
Not very important: 1171 = 34.3%
Total: 3417 = 100%
Because these students were not a random sample from a larger population, and because statistics students may not represent other students on questions of religion, treat these 3417 students as a population. Therefore, we know that for the population of elementary statistics students at Penn State from 2007 to 2010, 21.4% felt that religion was very important in their lives.
a. Based on the results in Example, can we conclude that this percentage differs from the percentage of the population of all adult Americans who felt that religion was very important in their lives in December 2009? Explain, taking into account the margin of error for the survey in Example.
b. Based on the preceding results and those in Example, answer the question in part (a) for the percentage who felt religion was fairly important and for the percentage who felt it was not very important.
c. Write a short news article comparing the two surveys as if you were writing it for the student newspaper.
d. Suppose we believe that the Penn State sample is representative of all students in the academic programs that require the elementary statistics course, and thus treat it as a sample from a larger population. Calculate an approximate 95% confidence interval for the population proportion that would say that religion is very important in their lives.
Example: The Importance of Religion for Adult Americans For a Gallup poll conducted December 11-13, 2009, a random sample of n = 1025 adult Americans was asked, "How important would you say religion is in your own life: very important, fairly important, or not very important?" (https://www.pollingreport.com/religion.htm, March 2, 2010). The percentages that selected each response were as follows:
Very important: 56%
Fairly important: 25%
Not very important: 19%
Conservative margin of error: [1/(√1025)] = .03 or .03 x 100% = 3%