Question

An experiment is conducted to determine whether there is a difference among the mean increases in growth produced by five strains (A, B, C, D and E) of growth hormones for plants. The experimental material consists of 20 cuttings of a shrub (all of equal weight), with four cuttings randomly assigned to each of the five different strains. The increases in weight for each cutting along with the sample mean and sample standard deviation of each group are given in the table below.

A | B | C | D | E | |

Plant 1 | 1313 | 2222 | 2525 | 1414 | 1111 |

Plant 2 | 1717 | 2323 | 2020 | 1010 | 99 |

Plant 3 | 1010 | 1515 | 2424 | 1919 | 88 |

Plant 4 | 1313 | 3030 | 2020 | 1818 | 1313 |

Mean | 13.2513.25 | 22.522.5 | 22.2522.25 | 15.2515.25 | 10.2510.25 |

Standard Dev. | 2.87232.8723 | 6.13736.1373 | 2.63002.6300 | 4.11304.1130 | 2.21742.2174 |

It is also given that the overall mean = 16.7.

Compute the following:

(a) SSTR==

(b) SSE ==

(c) MSTR ==

(d) MSE ==

(e) F ==

Answer #1

Reorganise the data in the format given below and import in R.

Run the following code:

summary(aov(dat$`Weight Increase`~dat$Strains+dat$Plants))

**Output:**

Df SS MS F value Pr(>F)

dat$Strains(TR) 4 7360137 1840034 8.703 0.00155 **

dat$Plants 3 868871 289624 1.370 0.29904

Residuals(Error) 12 2537193 211433

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

**Reorganised Data:**

Plants |
Strains |
Weight Increase |

Plant 1 | A | 1313 |

Plant 1 | B | 2222 |

Plant 1 | C | 2525 |

Plant 1 | D | 1414 |

Plant 1 | E | 1111 |

Plant 2 | A | 1717 |

Plant 2 | B | 2323 |

Plant 2 | C | 2020 |

Plant 2 | D | 1010 |

Plant 2 | E | 99 |

Plant 3 | A | 1010 |

Plant 3 | B | 1515 |

Plant 3 | C | 2424 |

Plant 3 | D | 1919 |

Plant 3 | E | 88 |

Plant 4 | A | 1313 |

Plant 4 | B | 3030 |

Plant 4 | C | 2020 |

Plant 4 | D | 1818 |

Plant 4 | E | 1313 |

An experiment is conducted to determine whether there is a
differnce among the mean increases in growth produced by five
strains (A, B, C, D and E) of growth hormones for plants. The
experimental material consists of 20 cuttings of a shrub (all of
equal weight), with four cuttings randomly assigned to each of the
five different strains. The increases in weight for each cutting
along with the sample mean and sample standard deviation of each
group are given in...

An experiment is conducted to determine whether there is a
differnce among the mean increases in growth produced by five
strains (A, B, C, D and E) of growth hormones for plants. The
experimental material consists of 20 cuttings of a shrub (all of
equal weight), with four cuttings randomly assigned to each of the
five different strains. The increases in weight for each cutting
along with the sample mean and sample standard deviation of each
group are given in...

An experiment is conducted to determine whether there is a
differnce among the mean increases in growth produced by five
strains (A, B, C, D and E) of growth hormones for plants. The
experimental material consists of 20 cuttings of a shrub (all of
equal weight), with four cuttings randomly assigned to each of the
five different strains. The increases in weight for each cutting
along with the sample mean and sample standard deviation of each
group are given in...

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6868
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1111
1919
88
1010
2525
2424
2222
66
2323
1616
99
55
33
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2020
4444
3131
3232
1717
2626
1414
8282
1313
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What is the data set's level of measurement? Explain your
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