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Statistics and Low Pitched Singers

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Statistics and Low Pitched Singers
Rebecca Verian 2577648
Context:
π 1: There is no significant difference between the mean heights of the singers. π2: The average of heights of high pitched voices is equal. π3: The average of heights of low pitched voices is equal.
Conditions:
* There are 39 cases. * Based on the graph gotten the average heights of Soprano are 64.25 inches. * The average heights of the Alto singers are 64.88 inches. * The Tenor singers had an average height of 69.15 inches. * The mean of the bass singers is 70.17 inches.
Calculations and Conclusions: Skewness Kurtosis | N | Minimum | Maximum | Mean | Stats | Std Error | Stats | Std Error | Soprano | 36 | 60 | 68 | 64.25 | -.496 | .393 | -.445 | .768 | Alto | 35 | 60 | 72 | 64.8857 | .313 | .398 | -.089 | .778 | Tenor | 20 | 64 | 76 | 69.15 | .398 | .512 | -.519 | .992 | Bass | 39 | 66 | 75 | 70.7179 | .104 | .378 | -.373 | .741 | Valid N | 20 | | | | | | | |

The Sopranos and Altos are considered high pitch and the Tenor and Bass are low pitched. The high pitch singers have less variations of height compared to the low pitched.
H0: The average of heights of all the four singers is equal to or the same.
H1: At least one group of singers has different average number of heights.
ANOVA
| Sum of Squares | df | Mean Square | F | Sig | Between Groups | 1058.529 | 3 | 352.843 | 55.800 | .000 | Within Groups | 796.740 | 126 | 6.323 | | | Total | 1855.269 | 129 | | | |

Testing π1: Ho: The average heights of high pitched voice parts singers are same. H1: The average heights of high pitched voice parts singers are not equal level of significance. Assume level of significance is a=0.05
ANOVA
| Sum of Significance | df | Mean Square | F | Sig | Between Groups | 783.139 | 1 | 783.139 | 170.834 | .000 | Within Groups | 334.647 | 73 | 4.584 | | | Total | 1117.787 | 74 | | | |

The p-value in the above table is less than the level
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