Math / Data & Statistics

QuestionTest 3 (Chapters 7 -9) om/Student/PlayerTest.aspx?testId=2643628178.centerwin=yes
A study of all the studonts at a small college showed a mean age of 20.5 and a standard deviation of 1.8 years a. Are these numbers statistics or parameters? Explain. b. Labol both numbers with their appropriate symbol (such as $\overline{\mathrm{x}}, \mu, \mathrm{s}$ , or $\sigma$ ). a. Choose the correct answer below. A. The numbers are statistics because they are estimates and not certain. B. The numbers are parameters because they are for all the students, not a sample. C. The numbers are statistics because they are for all the students, not a sample. D. The numbers are parameters because they are estimates and not certain. b. Choose the correct labels below. $\square$ $=20.5$ $\square$ $=1.8$ Assessment Details Calculator Webcam Chat Support

Studdy Solution

STEP 1

What is this asking? We need to determine if the given mean and standard deviation describe a whole group or just a sample, and then label them with the right symbols. Watch out! Don't mix up parameters (for populations) and statistics (for samples)!
Also, make sure to use the correct symbols for mean and standard deviation, distinguishing between population and sample.

STEP 2

1. Identify if the values are statistics or parameters.
2. Label the values with the appropriate symbols.

STEP 3

A parameter describes a characteristic of an entire population, while a statistic describes a characteristic of a sample taken from a population.

STEP 4

The problem states "A study of all the students at a small college...".
This indicates we're dealing with the entire population of students at the college.

STEP 5

Since the mean and standard deviation are calculated from the entire population, they are parameters.

STEP 6

The symbol for the population mean is $\mu$ , and the symbol for the population standard deviation is $\sigma$ .
The symbol for the sample mean is $\overline{x}$ , and the symbol for the sample standard deviation is $s$ .

STEP 7

We know from the previous step that we're working with population parameters.
The mean age of 20.5 is represented by $\mu = 20.5$ .
The standard deviation of 1.8 years is represented by $\sigma = 1.8$ .

STEP 8

a. The numbers are parameters because they describe the entire population of students at the small college.
This corresponds to answer choice B. b. The correct labels are $\mu = 20.5$ and $\sigma = 1.8$ .

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Studdy Solution

STEP 1

STEP 2

1. Identify if the values are statistics or parameters.
2. Label the values with the appropriate symbols.

STEP 3

A parameter describes a characteristic of an entire population, while a statistic describes a characteristic of a sample taken from a population.

STEP 4

The problem states "A study of all the students at a small college...".
This indicates we're dealing with the entire population of students at the college.

STEP 5

Since the mean and standard deviation are calculated from the entire population, they are parameters.

STEP 6

The symbol for the population mean is $\mu$ , and the symbol for the population standard deviation is $\sigma$ .
The symbol for the sample mean is $\overline{x}$ , and the symbol for the sample standard deviation is $s$ .

STEP 7

We know from the previous step that we're working with population parameters.
The mean age of 20.5 is represented by $\mu = 20.5$ .
The standard deviation of 1.8 years is represented by $\sigma = 1.8$ .

STEP 8

a. The numbers are parameters because they describe the entire population of students at the small college.
This corresponds to answer choice B. b. The correct labels are $\mu = 20.5$ and $\sigma = 1.8$ .

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Studdy Solution

STEP 1

STEP 2

1. Identify if the values are statistics or parameters.2. Label the values with the appropriate symbols.

STEP 3

A **parameter** describes a characteristic of an entire **population**, while a **statistic** describes a characteristic of a **sample** taken from a population.

STEP 4

The problem states "A study of *all* the students at a small college...".This indicates we're dealing with the entire population of students at the college.

STEP 5

Since the mean and standard deviation are calculated from the *entire* population, they are **parameters**.

STEP 6

The symbol for the **population mean** is μ\muμ, and the symbol for the **population standard deviation** is σ\sigmaσ.The symbol for the **sample mean** is x‾\overline{x}x, and the symbol for the **sample standard deviation** is sss.

STEP 7

We know from the previous step that we're working with **population parameters**.The **mean age** of **20.5** is represented by μ=20.5\mu = 20.5μ=20.5.The **standard deviation** of **1.8** years is represented by σ=1.8\sigma = 1.8σ=1.8.

STEP 8

a. The numbers are **parameters** because they describe the entire population of students at the small college.This corresponds to answer choice *B*. b. The correct labels are μ=20.5\mu = 20.5μ=20.5 and σ=1.8\sigma = 1.8σ=1.8.

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1. Identify if the values are statistics or parameters.
2. Label the values with the appropriate symbols.

A parameter describes a characteristic of an entire population, while a statistic describes a characteristic of a sample taken from a population.

The problem states "A study of all the students at a small college...".
This indicates we're dealing with the entire population of students at the college.

Since the mean and standard deviation are calculated from the entire population, they are parameters.

The symbol for the population mean is $\mu$ , and the symbol for the population standard deviation is $\sigma$ .
The symbol for the sample mean is $\overline{x}$ , and the symbol for the sample standard deviation is $s$ .

We know from the previous step that we're working with population parameters.
The mean age of 20.5 is represented by $\mu = 20.5$ .
The standard deviation of 1.8 years is represented by $\sigma = 1.8$ .

a. The numbers are parameters because they describe the entire population of students at the small college.
This corresponds to answer choice B. b. The correct labels are $\mu = 20.5$ and $\sigma = 1.8$ .