The Pew Research Center conducted a survey of a random sampl

The Pew Research Center conducted a survey of a random sample of U.S. adults in August 15-25, 2014. One question that the adults were asked was \"Does a science sometimes conflict with your own religious beliefs?\" Out of 2,002 adults, 600 responded yes, 1361 said no, and 41 said they didn\'t know. We are interested in adults who would respond yes, that science sometimes conflicts with their own religious beliefs.

a) what is the population?

b) what is the sample?

c) describe the parameter in words. do we know the vaule of the parameter? if yes, provide the value

d) describe the statistic in words. do we know the value of the statistic? if yes, provide the value

e) in order to make appropriate inferences, conditions need to be met to construct and interpret confidence intervals. for confidence intervals of a proportion, we need to have a random sample and both np and n(1-p) need to be greater than or equal to 15. are the conditions for constructing a confidence interval for a population based on this sample satisfied? support your answer

f) construct and interpret a 95% confidence interval for the population proportion who would say that science sometimes conflicts with their own religious beliefs

g) Based on your confidence interval in f, would you conclude that less than 50% of all adults in the U.S. would answer yes?

h) Based on your confidence in interval f, would you conclude that less than a third of all adults in the U.S. would answer yes?

i) How would a 90% confidence interval compare to the one you constructed in c? You should comment on the centers of the intervals and the widths of the intervals. Note: you do not need to construct a 90% confidence interval to answer

Solution

a) Population is total number of adults (age 15-25) in US - 2014.

Defintion: Population is known as a well-defined collection of individuals or objects known to have similar characteristics. All individuals or objects within a certain population usually have a common, binding characteristic or trait.

b) Sample is 2002 adults out of total number of adults (15-25) in US-2014

Definition: A sample is simply a subset of the population. The concept of sample arises from the inability of the researchers to test all the individuals in a given population. The sample must be representative of the population from which it was drawn and it must have good size to warrant statistical analysis.

c) A parameter is a measurable characteristic of a population, such as a mean or a standard deviation etc.

In our survey, Parameter is Population Proportion P = No. of reponds(adults) say Yes in the population / To no. of adults in US.

d) A statistic is a measurable characteristic of a sample such as sample mean or sample sd etc.

In our survey, Statistic is sample proportion p = No. of reponds(adults) say Yes in the sample / To no. of adults in survey = 600 / 2002 = 0.299 = 0.30(appr) = 30% of adults say Yes in the sample.