Question

A teacher predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores follow:

group |
test scores |
|||||||

1) constant sound |
7 |
8 |
6 |
8 |
6 |
6 |
7 |
9 |

2) random sound |
5 |
5 |
3 |
4 |
4 |
7 |
2 |
6 |

3) no sound |
2 |
4 |
5 |
1 |
2 |
1 |
4 |
4 |

**One-way ANOVA: Score versus Sound**

Source DF SS MS F P

Sound 73.58

Error 43.75

Tukey 95% Simultaneous Confidence Intervals

All Pairwise Comparisons among Levels of Sound

Individual confidence level = 98.00%

Sound = 1 subtracted from:

Sound Lower Center Upper ----+---------+---------+---------+-----

2 -4.442 -2.625 -0.808 (-------*------)

3 -6.067 -4.250 -2.433 (------*------)

----+---------+---------+---------+-----

-5.0 -2.5 0.0 2.5

Sound = 2 subtracted from:

Sound Lower Center Upper ----+---------+---------+---------+-----

3 -3.442 -1.625 0.192 (-------*------)

----+---------+---------+---------+-----

-5.0 -2.5 0.0 2.5

2. At a 5% level of significance, is there sufficient sample evidence to show that at least two of the means differ?

3. Use the Tukey pairwise comparisons (see printout) to determine which type of sound is best for effective learning.

Answer #1

**Answer:**

2. The ANOVA table is:

Source | DF | SS | MS | F | P |

Sound | 2 | 73.58 | 36.79 | 17.65 | 0.00 |

Error | 21 | 43.75 | 2.083 | ||

Total | 23 | 117.33 |

At a significance level of 0.05 we reject Ho as p-value is less than 0.05

3. Using the pairwise confirmation, the tests are different if the confidence interval doesn't contain 0.

Thus Constant sound(1) differs from random sound(2) no and sound (3).

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