Algebra 2B Unit 8 Review Conclusions from Sample Data

Match each term with its definition

• Spread of sample results

• Sample

• Using a sample to draw a conclusion about a population

• Statistical inference

• How much a sample result might differ

• Margin of error

• The entire group being studied

• Population

• A subgroup actually surveyed or studied

• Sampling distribution

The height, in inches, of six randomly selected girls from the school’s basketball team were recorded as follows:

{64, 67, 65, 71, 73, 69}.

Calculate x̅, the sample mean height to the nearest inch.

Mathematical Equivalence

ON

Given a standard deviation of 17.8 and a sample size of 23.

What is the standard error?

Round to the nearest hundredth.

Mathematical Equivalence

ON

The data contained in the table shows the number of Americans between 15 and 19 years old in 5 of the largest states compared to the overall population of the state. Treating each state as a sample of the U.S. population, what is the best estimate of the population proportion of the number of Americans 15 to 19 years old?

• 0.062

• 0.064

• 0.066

• 0.074

Which histogram represents a sample distribution of the given sample proportions?

• 
• 
• 
• 

As the sample size (n) increases, the sample proportion more closely approximates the population proportion.

• True
• False

Mr. John gave an exam to his students. The table shows their exam scores in decimal form. Given the table of 100 scores of students from the exam, which scores fall within two standard deviations of the mean? Write your answer as an interval. Given: s=0.13 and x̅=0.45

​ ​ ​ (a)   ≤ ​ (b)   ≤ ​ (c)  

• 0.19
• x̅
• 0.71
• 0.32
• 0.58
• σ

A histogram displays the sampling distribution of sample proportions based on a survey asking people what type of phones they own. The graph shows 10 sample proportions for one specific brand.

Based on the histogram, can you determine the exact percentage of people in the population who own that brand of phone?

• Yes, because the highest bar on the histogram shows the population proportion.

• Yes, because the average of the sample proportions must be the exact population proportion.

• No, because the histogram only shows individual people's responses, not group proportions.

• No, because a sampling distribution only shows how sample results vary, not the exact population value.

The figure shows how the distribution of a sampling proportion appears when the sample size is n=10, n=100, n=1000. How does the range of variability and the shape of the distribution change as the sample size becomes larger?

• As sample size increases, the range or variability decreases, and the shape of the distribution becomes more symmetric.

• As sample size increases, the range or variability increases, and the shape of the distribution becomes more symmetric.

You are a pollster conducting a survey to estimate the proportion of voters who support a certain candidate in an upcoming election. You take a random sample of 500 voters and find that 280 of them support the candidate. Estimate the population proportion of the voters who support the candidate using two standard errors. Round your answer to two decimal places.

(a)   ≤ p ≤ ​ ​ (b)  

• 0.52
• 0.54
• 0.56
• 0.58
• 0.60
• 0.62