Question

Researchers want to determine whether listening to music affects the speed at which teenagers read. A group of 20 teenagers were chosen at random and asked to read the same book for 30 minutes. Half of the participants read in silence (Group A) and the other half read while listening to music (Group B). The number of pages each teenager read was recorded.

Group A: 38, 31, 30, 28, 40, 20, 26, 32, 34, 31
Group B: 19, 26, 30, 28, 32, 31, 36, 25, 29, 14

1. Find the mean of each groyp and the difference of means.

Mean of Group A =

Mean of group B =

Difference of means =

2. Which of the following is true about the mean of the entire sample?

A. It is less than the mean of group B
B. It is greater than the mean of group A.
C. It is in between the means of group A and group B
D. There is not enough information to determine the answer

3. Find the range fir each group and the range for the entire sample.

Range for group A =

Range for group B =

Range for the entire sample =

4. Fill in the blank

The range of the entire sample is always _ than the range of each group.

A. Less than
B: greater than
C. equal to

Answer 1

Let's go through the questions step by step.

### 1. Finding the Means and the Difference of Means

**Group A:**
- Values: 38, 31, 30, 28, 40, 20, 26, 32, 34, 31
- Mean of Group A = (38 + 31 + 30 + 28 + 40 + 20 + 26 + 32 + 34 + 31) / 10

Calculating the sum:
\[
38 + 31 + 30 + 28 + 40 + 20 + 26 + 32 + 34 + 31 = 338
\]

Then, calculating the mean:
\[
\text{Mean of Group A} = 338 / 10 = 33.8
\]

**Group B:**
- Values: 19, 26, 30, 28, 32, 31, 36, 25, 29, 14
- Mean of Group B = (19 + 26 + 30 + 28 + 32 + 31 + 36 + 25 + 29 + 14) / 10

Calculating the sum:
\[
19 + 26 + 30 + 28 + 32 + 31 + 36 + 25 + 29 + 14 = 338
\]

Then, calculating the mean:
\[
\text{Mean of Group B} = 338 / 10 = 33.8
\]

**Difference of Means:**
\[
\text{Difference of Means} = \text{Mean of Group A} - \text{Mean of Group B} = 33.8 - 33.8 = 0
\]

### Results:
- Mean of Group A = 33.8
- Mean of Group B = 33.8
- Difference of Means = 0

### 2. Which of the following is true about the mean of the entire sample?
To find the overall mean, we add the means of both groups and divide by 2 (since they have the same number of samples):

\[
\text{Mean of the entire sample} = (33.8 + 33.8) / 2 = 33.8
\]

Now comparing:
- The mean of the entire sample (33.8) is equal to the means of both groups.

- Thus neither of the options A, B, or C are true, but technically the mean is not "greater than" Group A and is not "less than" Group B, the most correct selection would be option **C**, as stated in the prompt of "in between," implies that the means must be distinct, which is not the case here.

### 3. Finding the Range

**Group A:**
- Minimum: 20
- Maximum: 40
- Range for Group A = Maximum - Minimum = 40 - 20 = 20

**Group B:**
- Minimum: 14
- Maximum: 36
- Range for Group B = Maximum - Minimum = 36 - 14 = 22

**Entire Sample:**
- Minimum: 14 (from Group B)
- Maximum: 40 (from Group A)
- Range for the entire sample = Maximum - Minimum = 40 - 14 = 26

### Results:
- Range for Group A = 20
- Range for Group B = 22
- Range for the entire sample = 26

### 4. Fill in the blank

The range of the entire sample is always **B. greater than** the range of each group. (This is because the entire sample includes all values from both groups, thus it is likely to span a larger range.)

### Summary of Answers:
1.
- Mean of Group A = 33.8
- Mean of Group B = 33.8
- Difference of means = 0

2. C. It is in between the means of group A and group B

3.
- Range for Group A = 20
- Range for Group B = 22
- Range for the entire sample = 26

4. B: greater than