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Chapter 8: Problem 1

Explain the difference between a population characteristic and a statistic.

Short Answer

Expert verified
A population characteristic (or parameter) is a value that accurately represents a certain aspect of an entire population, while a statistic is a variable that represents a certain aspect of a sample taken from the population. The former always stays the same and pertains to the whole group, while the latter can vary as it is based on a subset of the group.

Step by step solution

01

Define Population Characteristic

A population characteristic, also known as a parameter, is a value that accurately represents a particular aspect of an entire population. It is a fixed and unknown value. For example, the mean income of every family in a country.
02

Define Statistic

A statistic, on the other hand, is a value that represents a particular aspect of a sample taken from a population. It鈥檚 a random variable that varies from sample to sample. For instance, the mean income of a set of randomly selected families in a country.
03

Highlight the Difference

The main difference between a population characteristic and a statistic is that the former relates to all the members of a population while the latter relates to a sample of the population. So, a population characteristic is always fixed and accurate, whereas a statistic can vary because it only represents part of the population.

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Most popular questions from this chapter

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5 . a. What are the mean and standard deviation of the \(\bar{x}\) sampling distribution? Describe the shape of the \(\bar{x}\) sampling distribution. b. What is the approximate probability that \(\bar{x}\) will be within \(0.5\) of the population mean \(\mu\) ? c. What is the approximate probability that \(\bar{x}\) will differ from \(\mu\) by more than \(0.7\) ?

Consider a population consisting of the following five values, which represent the number of video rentals during the academic year for each of five housemates: \(\begin{array}{lll} 8 & 14&16 & 10 & 11\end{array}\) a. Compute the mean of this population. b. Select a random sample of size 2 by writing the numbers on slips of paper, mixing them, and then selecting \(2 .\) Compute the mean of your sample. c. Repeatedly select samples of size 2 , and compute the \(\bar{x}\) value for each sample until you have the results of 25 samples. d. Construct a density histogram using the \(25 \bar{x}\) values. Are most of the \(\bar{x}\) values near the population mean? Do the \(\bar{x}\) values differ a lot from sample to sample, or do they tend to be similar?

The amount of money spent by a customer at a discount store has a mean of $$\$ 100$$ and a standard deviation of $$\$ 30.$$ What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $$\$ 5300 ?$$ (Hint: The total will be more than \(\$ 5300\) when the sample average exceeds what value?)

Let \(x_{1}, x_{2}, \ldots, x_{100}\) denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean \(50 \mathrm{lb}\) and variance \(1 \mathrm{lb}^{2}\). Let \(\bar{x}\) be the sample mean weight \((n=100)\). a. Describe the sampling distribution of \(\bar{x}\). b. What is the probability that the sample mean is between \(49.75 \mathrm{lb}\) and \(50.25 \mathrm{lb}\) ? c. What is the probability that the sample mean is less than \(50 \mathrm{lb}\) ?

An airplane with room for 100 passengers has a total baggage limit of 6000 lb. Suppose that the total weight of the baggage checked by an individual passenger is a random variable \(x\) with a mean value of \(50 \mathrm{lb}\) and a standard deviation of \(20 \mathrm{lb}\). If 100 passengers will board a flight, what is the approximate probability that the total weight of their baggage will exceed the limit? (Hint: With \(n=100\), the total weight exceeds the limit when the average weight \(\bar{x}\) exceeds \(6000 / 100\).)
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