Question

diane publishes a blog on bird - watching, with field notes and pictures of her trips around the country. recently she decided to conduct a poll among 600 of her subscribers, and found that 71% of those polled have liked at least one of her blogs, they have posted an average of 1.8 comments per blog, and 128 have liked all of her blogs. later she found out that her website already has this information for all of her subscribers. according to her website, she has a total of 12,683 subscribers, of whom 68% have liked at least one of her blogs, they have posted an average of 1.5 comments per blog, and 3781 have liked all of her blogs.
(a) for diane’s blog poll, identify the population and the sample.
population: all the subscribers to diane’s blog
sample: the 600 subscribers diane polled
(b) choose whether each number described below is a parameter or a statistic for diane’s blog poll.

number	parameter	statistic
the 68% of all the subscribers to diane’s blog who like at least one blog	○	○
the 3781 subscribers among all the subscribers to diane’s blog who like all of her blogs	○	○

Explanation:

Part (a)

Step 1: Define population and sample

• Population: The entire group of individuals or objects that we are interested in studying. In this case, it is all the subscribers to Diane's blog.
• Sample: A subset of the population that is selected for study. Here, it is the 600 subscribers Diane polled.

Part (b)

Step 1: Recall the definitions of parameter and statistic

• Parameter: A characteristic of a population.
• Statistic: A characteristic of a sample.

Step 2: Analyze each number

• The average of 1.8 comments per blog that the 600 subscribers polled have posted: Since it is about the sample (600 subscribers), it is a statistic.
• The 68% of all the subscribers to Diane's blog who like at least one blog: Since it is about the population (all subscribers), it is a parameter.
• The 3781 subscribers among all the subscribers to Diane's blog who like all of her blogs: Since it is about the population (all subscribers), it is a parameter.

Answer:

(a) Population: All the subscribers to Diane's blog; Sample: The 600 subscribers Diane polled.
(b)

• The average of 1.8 comments per blog that the 600 subscribers polled have posted: Statistic.
• The 68% of all the subscribers to Diane's blog who like at least one blog: Parameter.
• The 3781 subscribers among all the subscribers to Diane's blog who like all of her blogs: Parameter.