Question

The effects of three concentrations of the ripening hormone (ethylene) were tested on tomato yield and quality. Five tomato cultivars (Shady Lady, Merced, Santa, Chiquita, and Celebrity) were grown in 5 replications in the field. The hormone was applied 4 weeks after flowering. Fruits were harvested 4, 5 and 6 weeks after the hormone application. Number of fruits per plot was counted, and fruits of each plot were classified to three groups of red, yellow-red and yellow. Fruit yield (kg/plot) and sugar concentration were measured. Fruit texture and taste were surveyed in a population of 50 people. For the survey, a sample of the fruits from each plot was given to people to eat and score taste from 1 to 10, and fruit texture from 1-5.

Identify the:

Problem

1. Hypothesis:
   1. H₀:
2. 2. H₁:

Experimental unit:

Experimental material:

Control variable(s)

Independent variable(s):

Dependent variable(s):

7. 1. Quantitative variable(s):
   2. Qualitative variable(s):
8. 1. Continuous variable(s):
   2. Discrete variable(s):

Answer 1

All the parts of the question are answered below:

Experimental Unit and its Hypothesis

I shall do One way Anova twice in this regard, in order to analyse:

1. Whether the mean rating of taste for all the three groups is same or different.

2. Whether the mean rating of texture for all the three groups is same or different.

Case 1: (for taste)

H₀ : U₁ = U₂ = U₃

H_a : All the means are not equal

Case 2: (for texture)

H₀ : U₁ = U₂ = U₃

H_a : All the means are not equal

Experimental Material

Here, 50 people will be surveyed and all of them are required to provide their respective rating for the fruits (for the three different groups) as per requirement (for taste and texture) on a predetermined scale.

A sample collection of data is shown below just for reference purpose.

Sample rating for the taste score (on a scale of 1-10).

Similar can be done for texture on a rating of 1 to 5.

Take one group as a dependent and the other two as an independent variable in this experiment.

The analysis will be like:

Let us take a sample output of Excel in this regard as shown below:

Kindly note that this is a sample output where we are comparing the data of three different groups.

Here, you can see that the P value is 0.63047

If we take the confidence level as 95% (Alpha will 0.05)

Alpha = 1 - Confidence Level

= 1 - 0.95

= 0.05

Alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true.

Here as the P value is larger than 0.05, so we can state that the null hypothesis is accepted. This is because there is no such significant difference in the means of all the three groups.

Similarly for your case, if there is no such significant difference than you can state that the three groups of fruits has almost the same taste and texture.

Quantitative variables are shown above. Qualitative, Discrete and Continuous variables are not required for this analysis (Anova).

End of the Solution...