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Chapter 7: Problem 3

For Exercises 1 to \(4,\) identify the population, the parameter, the sample, and the statistic in each setting. Hot turkey Tom is cooking a large turkey breast for a holiday meal. He wants to be sure that the turkey is safe to eat, which requires a minimum internal temperature of \(165^{\circ} \mathrm{F} .\) Tom uses a thermometer to measure the temperature of the turkey meat at four randomly chosen points. The minimum reading in the sample is \(170^{\circ} \mathrm{F} .\)

Short Answer

Expert verified
Population: Turkey breast; Parameter: Minimum temperature; Sample: Four points; Statistic: 170掳F.

Step by step solution

01

Identify the Population

The population in this scenario refers to the entire turkey breast that Tom is cooking. It represents all possible points within the turkey where the temperature could be measured.
02

Determine the Parameter

The parameter is the minimum internal temperature of the entire turkey breast that Tom is interested in finding to ensure it's safe to eat. This parameter is the unknown minimum temperature of the turkey as a whole.
03

Define the Sample

The sample is the set of four random points within the turkey breast where Tom measures the temperature using a thermometer. These points serve as representative spots to gauge the turkey's overall temperature.
04

Identify the Statistic

The statistic in this context is the result derived from the sample, specifically, the minimum temperature recorded from the four measurement points, which is 170掳F.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population
In statistical terms, the concept of "Population" represents the complete set of items or individuals that are being studied. In our exercise scenario, the population is the entire turkey breast that Tom is cooking for the holiday meal. When thinking about populations, it refers to all members within a defined group in which we are interested, and from which we seek to draw conclusions.
  • The population isn't just a general idea; it is specifically defined by the context of the study.
  • In statistics, the population can refer to people, objects, events, or even measurements like temperatures, which in this case is every point within the turkey breast.
Understanding what constitutes a population is crucial because it determines the scope and relevance of our statistical insights.
Parameter
A "Parameter" is a measurable characteristic of a population, such as a mean or a total. In the exercise example involving Tom and his turkey, the parameter is the minimum internal temperature of the turkey breast, representing the specific attribute Tom is eager to ensure for food safety. Parameters are often unknown and are the target of our estimations with statistics.
  • Parameters are theoretical values regarding a population, often challenging to obtain.
  • In many cases, parameters remain an unknown aspect that we aim to estimate or test using statistics from samples.
In summary, understanding parameters helps in setting the goals for any statistical analysis or measurement we perform.
Sample
A "Sample" refers to a subset of the population that we select to measure and analyze for statistical purposes. Instead of examining the entire turkey breast, Tom takes the temperature at just four randomly chosen points. These points form the sample and give us insights into the temperature throughout the turkey in a more efficient manner than checking the entire breast.
  • Samples are practical tools for gathering data due to limitations in resources or time.
  • Effective sampling involves ensuring these subsets are representative of the larger population.
Samples help in making inferences about the population without the need to evaluate every individual member.
Statistic
A "Statistic" is a measurable characteristic derived from a sample, providing an estimate or piece of information about the parameter. In Tom鈥檚 scenario, the statistic is the minimum temperature recorded among the four measured points, which was 170掳F. This recorded statistic is used to infer about the population, in this case, the entire turkey breast.
  • Statistics are helpful in estimating unknown parameters within populations through sampled observations.
  • The effectiveness of a statistic depends heavily on how representative and unbiased the sample is.
By understanding statistics, we can draw conclusions and make data-informed decisions without needing to analyze every part of a population directly.

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Most popular questions from this chapter

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In Exercises 33 and \(34,\) explain why you cannot use the methods of this section to find the desired probability. Hispanic workers A factory employs 3000 unionized workers, of whom 30\(\%\) are Hispanic. The 15 -member union executive committee contains 3 Hispanics. What would be the probability of 3 or fewer Hispanics if the executive committee were chosen at random from all the workers? CHALLENGE: See if you can compute the probability using another method.

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