Question

1. Describe each of the following symbols. What does the symbol...

1. Describe each of the following symbols.

What does the symbol represent? Is the symbol describing a sample statistic or a population parameter? N , n , π , p̂ , µ , x̅, σ , s , 𝜎𝜎2, 𝑠𝑠2, ρ , r , 𝛽𝛽1 , 𝑏𝑏1


(#2-13)

Determine if the numbers in the following clips from magazines and newspapers are describing a population parameter or a sample statistic. In each case, give the symbol used for the parameter or statistic. (N , n , π , p̂ , µ , x̅, σ , s , 𝜎𝜎2, 𝑠𝑠2, ρ , r , 𝛽𝛽1 , 𝑏𝑏1)


2. "Our study found that of the 200 people tested in the sample, only 3% showed side effects to the medication."

3. "It has been speculated for years that the mean average height of all men is 69.2 inches, but our sample data disagrees with this. Our sample mean average was 69.5 inches."

4. "The standard deviation for all humans is about 1.8 degrees Fahrenheit. A random sample of 52 people found a standard deviation of 1.739 degrees Fahrenheit".

5. "We tested a sample of 300 incoming college freshman and found that their mean average IQ was 101.9 with a standard deviation of 14.8".

6. "The mean average human body temperature has long been thought to be 98.6 degrees Fahrenheit, but our sample of 63 randomly selected adults had a mean average was 98.08".

7. "The mean average number of units that students take per semester is about 12, but when we took a random sample of 160 college students found that the mean average was 12.37 units."

8. "A public opinion poll showed that 47.2% of voters would vote for the candidate, but when the votes or entire population were counted we found that only 41.3% voted for the candidate."

13. "According to the 2015 U.S. census, approximately 78% of U.S. households own a computer. A random sample of 165 households found that 81.2% of them owned a computer." 

Answer & Explanation
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1. 

N - population size

n - sample size

π - population proportion

p - sample proportion

μ - population mean

xˉ - sample mean

σ - population standard deviation

s - sample standard deviation

σ2 - population variance

s2 - sample variance

ρ - linear correlation coefficient (population)

r - Pearson product moment correlation coefficient (sample)

β1 - slope of the simple linear regression model (population)

b1 - slope of the simple linear regression model (sample)

 

2. 

sample statistic: n and p^

n = 200 

p^=0.03 

 

3. 

population parameter: μ

μ=69.2 

sample statistic: xˉ

xˉ=69.5

 

4. 

population parameter: σ

σ=1.8

sample statistic: n and s

n = 52 

s=1.739 

 

5. 

sample statistic: n,xˉ,s'

n = 300 

xˉ=101.9 

s=14.8 

 

6. 

population parameter: μ

μ=98.6 

sample statistic: n,xˉ

n=63 

xˉ=98.08 

 

7. 

population parameter: μ

μ=12

sample statistic: n,xˉ

n=160 

xˉ=12.37 

 

8. 

population parameter: π

π=0.413 

sample statistic: p^

p^=0.472 

 

13. 

population parameter: π

π=0.78 

sample statistic: n,p^

n=165 

p^=0.812 

Step-by-step explanation

1. Describe each of the following symbols.

N - population size

It represents the number of individuals in a population.

n - sample size

It represents the number of individuals in a sample.

π - population proportion

It represents the percentage or the proportion of "success" in the population

p - sample proportion

It represents the percentage or the proportion of "success" in the sample

μ - population mean

It represents the mean in the population

xˉ - sample mean

It represents the mean in the sample

σ - population standard deviation

It represents the standard deviation in the population.

s - sample standard deviation

It represents the standard deviation in the sample

σ2 - population variance

It represents the variance in the population

s2 - sample variance

It represents the variance in the sample

ρ - linear correlation coefficient (population)

It represents the strength of the linear relationship existing between two variables in the population.

r - Pearson product moment correlation coefficient (sample)

It represents the strength of the linear relationship existing between two variables in the sample.

β1 - slope of the simple linear regression model (population)

It is a regression coefficient that gives the slope of the line

b1 - slope of the simple linear regression model (sample)

It is a regression coefficient that gives the slope of the line

 

2. "Our study found that of the 200 people tested in the sample, only 3% showed side effects to the medication."

sample statistic: n and p^

n = 200 since there are 200 people in the sample

p^=0.03 since 3% showed side effects to the medication

 

3. "It has been speculated for years that the mean average height of all men is 69.2 inches, but our sample data disagrees with this. Our sample mean average was 69.5 inches."

population parameter: μ

μ=69.2 since the mean average height of all men is 69.2 inches

sample statistic: xˉ

xˉ=69.5 since the sample mean average was 69.5 inches

 

4. "The standard deviation for all humans is about 1.8 degrees Fahrenheit. A random sample of 52 people found a standard deviation of 1.739 degrees Fahrenheit".

population parameter: σ

σ=1.8 since the standard deviation for all humans is about 1.8 degrees Fahrenheit

sample statistic: n and s

n = 52 since we have a random sample of 52 people

s=1.739 since the standard deviation of the random sample is 1.739

 

5. "We tested a sample of 300 incoming college freshman and found that their mean average IQ was 101.9 with a standard deviation of 14.8".

sample statistic: n,xˉ,s'

n = 300 since we have a sample of 300 incoming college freshman

xˉ=101.9 since we have a mean average of 101.9

s=14.8 since the standard deviation of 14.8

 

6. "The mean average human body temperature has long been thought to be 98.6 degrees Fahrenheit, but our sample of 63 randomly selected adults had a mean average was 98.08".

population parameter: μ

μ=98.6 since the mean average human body temperature is 98.6 degrees Fahrenheit

sample statistic: n,xˉ

n=63 since we have a sample of 63 adults

xˉ=98.08 since the sample has mean average 98.08

 

7. "The mean average number of units that students take per semester is about 12, but when we took a random sample of 160 college students found that the mean average was 12.37 units."

population parameter: μ

μ=12 since the mean average number of units that students take per semester is about 12

sample statistic: n,xˉ

n=160 since we took a random sample of 160 college students

xˉ=12.37 since the mean average of the random sample is 12.37 units

 

8. "A public opinion poll showed that 47.2% of voters would vote for the candidate, but when the votes or entire population were counted we found that only 41.3% voted for the candidate."

population parameter: π

π=0.413 since the 41.3% voted for the candidate when we counted the entire population

sample statistic: p^

p^=0.472 since public opinion poll showed that 47.2% of voters would vote for the candidate

 

13. "According to the 2015 U.S. census, approximately 78% of U.S. households own a computer. A random sample of 165 households found that 81.2% of them owned a computer." 

population parameter: π

π=0.78 since approximately 78% of U.S. households own a computer according to the census

sample statistic: n,p^

n=165 since we have a random sample of 165 households

p^=0.812 since the sample found that 81.2% of them owned a computer