# 1. Use the first six line of data only. Run an overall ANOVA to det...

## Question

1. Use the first six line of data only. Run an overall ANOVA to determine whether or not any cultivar has a different mean yield, or whether they are all the same. The run pairwise.t.test to compare all pairs of means. Check assumptions.
Do not write a full report. Just state each hypothesis, test it, draw a conclusion. You can write directly on the R sheet, as long as you make it easy to follow.

2. The treatments are the blades, and the blocks are the types of wood. You are interested in answering the question of whether or not the mean cutting time is the same for all blades. Check assumptions.
Again, do not write a full report. Just state each hypothesis, test it, draw a conclusion. You can write directly on the R sheet, as long as you make it easy to follow.
Background info: pine is the softest wood, and Kauri is the hardest. Jarrah is close to Kauri, but not quite as hard.

## Solution Preview

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Solution:

Purpose:

We want to see whether different cultivar has same mean yield or not.

Null and Alternative Hypotheses:

Null Hypothesis (Ho): There is no statistically significant difference in the population mean yield of different cultivar.

Alternative Hypothesis (Ha): There is a statistically significant difference in the population mean yield of different cultivar, at least one cultivar is different from another.

Mathematically;

Null Hypothesis (Ho): µ1 = µ2 = µ3 = µ4 = µ5 = µ6

Alternative Hypothesis (Ha): µi ≠ µj for some i ≠j

Level of significance = 0.05

Data:
production cultivar
1       1611    Wairau
2       1757    Wairau
3       1964    Wairau
4       2444    Wairau
5       1586 Caliverde
6       3071 Caliverde
7       2565 Caliverde
8       1547 Caliverde
9       1041    Ranger
10       3857    Ranger
11       934    Ranger
12       856    Ranger
13       1079    Vernal
14       2172    Vernal
15       539    Vernal
16       1310    Vernal
17       989    Dawson
18       1922    Dawson
19       455    Dawson
20       474    Dawson
21       2923    Kanza
22       5947    Kanza
23       3713    Kanza
24       2319    Kanza

Assumptions:

- Each group sample is drawn from a normally distributed population which is true in our case.
- All populations have a common variance.
- All samples are drawn independently of each other which is satisfied in our case.
- Within each sample, the observations are sampled randomly and independently of each other...

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