Question

at a tv assembling facility, the quality assurance (qa) department tested a random selection of 400 tvs assembled in march. the tested tvs had an average retail price of $425, 3.5% had some type of defect, and 8 did not power up at all. the plant manager compared that to the total of 5923 tvs that were assembled during the month of march. they had an average retail price of $355, 3.3% had been reported defective by customers, and 87 did not power up at all.
(a) for the qa departments tests, identify the population and the sample.
population: select
sample: select
(b) choose whether each number described below is a parameter or a statistic for the qa departments tests.
number parameter statistic
the 8 tvs of the random selection of 400 tvs that did not power up at all
the 3.3% of all the tvs assembled during the month of march reported defective
the average retail price of $425 of the random selection of 400 tvs

Explanation:

• Part (a):
• In statistics, the population is the entire group of individuals or items that we are interested in studying. Here, the QA department is interested in all the TVs assembled in March. So, the population is all \(5923\) TVs assembled in March.
• A sample is a subset of the population. The QA department tested a random selection of \(400\) TVs. So, the sample is the \(400\) TVs that were randomly selected and tested.
• Part (b):
• A statistic is a characteristic of a sample. The \(8\) TVs (out of the sample of \(400\) TVs) that did not power up and the average retail price of \(\$425\) (calculated from the sample of \(400\) TVs) are based on the sample. So, these are statistics.
• A parameter is a characteristic of a population. The \(3.3\%\) of all TVs (the entire population of \(5923\) TVs) reported defective is based on the population. So, this is a parameter.

Answer:

• (a)
• Population: All \(5923\) TVs assembled in March
• Sample: The \(400\) TVs that were randomly selected and tested
• (b)
• The \(8\) TVs of the random selection of \(400\) TVs that did not power up at all: Statistic
• The \(3.3\%\) of all the TVs assembled during the month of March reported defective: Parameter
• The average retail price of \(\$425\) of the random selection of \(400\) TVs: Statistic