Question

Three students wants to estimate the mean word length of the same book. To do this each student randomly chose 8 words from the book and recorded the lengths. The samples are shown in the table.Do not round your answers

Answer 1

Given -

To Find -

Range =?

Sample Mean =?

Step-by-Step Explanation -

(A).

1. Sample Mean :

`\begin{gathered} =\text{ }(8+7+5+9+8+9+8+7)/(8) \\ \\ =\text{ 7.625} \end{gathered}`

2. Sample Mean :

`\begin{gathered} =\text{ }(8+9+7+7+7+9+8+6)/(8) \\ \\ =\text{ 7.625} \end{gathered}`

3. Sample Mean :

`\begin{gathered} =\text{ }(9+6+7+6+9+6+8_+8)/(8) \\ \\ =\text{ }7.375 \end{gathered}`

(B). Range of the sample mean =

= 7.375 - 7.625

= -0.25

(C). Mean of sample Mean =

`\begin{gathered} =\text{ }(7.625+7.625+7.375)/(3) \\ \\ =\text{ 7.541} \\ \end{gathered}`

True Statements:

A Single sample mean will tend to be worse than the mean of the sample means.

{The more sample size, the more reliable}

The farther the range of the sample means is from 0, the less confident they can be in their estimate.

Final Answer -

(a) Sample Mean:

1) 7.625

2) 7.625

3) 7.375

(b) Range of the sample mean = -0.25

(c) True Statements:

A Single sample mean will tend to be worse than the mean of the sample means.

The farther the range of the sample means is from 0, the less confident they can be in their estimate.