Random Sampling and Word Length Analysis

In Lesson 14, Mrs. Apia teaches the importance of selecting a representative sample to generalize findings to a larger population. The lesson includes a coin toss activity to explore randomness and an analysis of word lengths in the poem 'Casey at Bat' to understand sampling and mean calculation. Students learn to differentiate between random and non-random samples and how to calculate the mean of a sample. The lesson concludes with a summary of key statistical concepts such as random sampling, population, and sample statistics.

Why is it important to select a sample randomly when trying to generalize to a larger population?

• To make the sample larger

• To ensure the sample is representative

• To make the sample more diverse

• To ensure the sample is biased

What pattern is typically observed in sequences created by students when asked to simulate random coin tosses?

• More tails than heads

• Long streaks of heads or tails

• Alternating heads and tails

• More heads than tails

What is a common characteristic of a truly random sequence?

• It has no streaks of the same outcome

• It includes streaks of three or more of the same outcome

• It has predictable patterns

• It alternates perfectly between outcomes

In the poem 'Casey at Bat', what is the population of interest when analyzing word lengths?

• All the words in the poem

• Only the shortest words

• A random selection of words

• Only the longest words

How is the mean word length calculated in a sample?

• By counting the number of words

• By adding the number of letters and dividing by the number of words

• By selecting the longest word

• By selecting the shortest word

Why might a randomly selected sample provide a better estimate of the population mean?

• It is always smaller than the population mean

• It is more likely to be representative of the population

• It is easier to calculate

• It is always larger than the population mean

What was the actual mean word length in the poem 'Casey at Bat'?

• 3.875 letters

• 6.3 letters

• 4.2 letters

• 5.25 letters

How can you ensure a sample is random when selecting words from a poem?

• Pick words from the beginning of the poem

• Choose words that you like

• Select words that are easy to spell

• Number each word and draw numbers randomly

What is a sample statistic in the context of this lesson?

• The longest word in the sample

• The mean number of letters in the sample

• The total number of words in the poem

• The shortest word in the sample

What is the main advantage of using a random sample over a non-random sample?

• It requires fewer resources

• It is more likely to be representative of the population

• It is easier to collect

• It always has a larger mean