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The PGA conducts a study in which they use a simple random sample of 600 golfers. They examine the data from the sample and calculate that 28% of them own golf clubs made in the USA. The 28% is the:

a) Population proportion.
b) Sample proportion.
c) Confidence interval.
d) Margin of error.

1 Answer

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Final answer:

The 28% mentioned in the study is the sample proportion, which is different from the population proportion, the confidence interval, and the margin of error.

Step-by-step explanation:

The percentage mentioned, 28%, is the statistic known as the sample proportion, representing the proportion of the 600 golfers in the simple random sample who own golf clubs made in the USA.

A population proportion would refer to this metric across the entire population of golfers, not just the sample studied. A confidence interval is a range derived from the sample statistic that is believed to contain the actual population proportion with a certain degree of confidence. The margin of error reflects the half-width of that confidence interval and indicates the maximum expected difference between the sample statistic and the population parameter.

In constructing confidence intervals, one would alter the margin of error and width of the interval depending on the chosen confidence level. For example, if one were to decrease the confidence level from 99 percent to 90 percent, the confidence interval would become narrower as the margin of error decreases, reflecting less certainty in the estimate. This is because a lower confidence level admits a higher probability of the interval not capturing the true population proportion.

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