Question

Three students want to estimate the mean word length of the same book. To do this, each student randomly chose 4 words from the book and recorded their lengths. The samples are shown in the table. (a)Fill in the sample means in the table. Do not round your answers. (number of letters) Sample mean 3, 3, 4, 7 - 8, 2, 3, 6 - 8, 5, 2, 4 (b)Use the table to calculate the range of the sample means. Range of sample means: (c)The students are going to use the sample means to estimate the mean word length in the book. Select all the true statements below. The mean of the sample means will tend to be a worse estimate than a single sample mean. A single sample mean will tend to be a worse estimate than the mean of the sample means. The closer the range of the sample means is to 0, the more confident they can be in their estimate. The farther the range of the sample means is from 0, the more confident they can be in their estimate.

Answer 1

The solutions to the questions are given below

a)

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)R =0.75

c)

• The mean of the sample means will tend to be a better estimate than a single sample mean.
• The closer the range of the sample means is to 0, the more confident they can be in their estimate.

What is the students are going to use the sample means to estimate the mean word length in the book.?

The table below shows sample means in the table.

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)

Generally, the equation for is  mathematically given as

variation in the sample means

R =maximum -minimum

R=4.25-3.5

R =0.75

c)

In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.

They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.

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