Question

QUESTION 5 a) Some people say if you want cut roses to last longer, you should add aspirin to the water. Others say add sugar. However, Aminah says adding 2 table spoon of bleach per one liter of water will work better than anything else. Design an experiment based on the following questions. i) State the hypothesis. (2 marks) ii) Determine the independent and dependent variables. 4 marks) ii) Identify the appropriate statistical analysis to be used and give the reason for your (4 marks) answer iv) State two parameters that need to be kept constant during the experiment. (4 marks)

Answer 1

(a)

(i)

Null Hypothesis: Duration of roses are same on applying aspirin, sugar or bleach. This means that aspirin, sugar or bleach has no effect or same effect on the duration of roses.

Alternative Hypothesis: At least on of those three has different effects than others. This means duration will be different on applying at least one of those three.

(ii)

Dependent variable: Duration of roses

Independent Variable: Aspirin, sugar or bleach.

(iii)

ANOVA analysis needs to be done for this hypothesis testing. Total sum of squares, Treatment sum of squares and error sum of squares are calculated. Finally F ration is calculated to compare with the table to conclude whether to reject or fail to reject null hypothesis.

(iv)

Two parameters are random error mean (zero) and variance ($\sigma^2$)

(b)

The confidence interval

$= [\bar x - z_{\alpha/2} * \frac{\sigma}{\sqrt n}, \bar x + z_{\alpha/2} * \frac{\sigma}{\sqrt n}]$

Given, $\bar x$ = 5.5, $\sigma$ = 0.6, $\alpha$ = 0.01

Now for $\alpha$ = 0.01 the value of $z_{\alpha/2}$ = 2.576

Putting these value we get the confidence Interval

$= [5.5 - 2.576 * \frac{0.6}{\sqrt {25}}, 5.5 + 2.576 * \frac{0.6}{\sqrt {25}}]$

= [5.191, 5.809]

(c)

(i)

Below is the scatterplot:

(ii)

From the scatterplot it is clearly seen that there is positive correlation between ages and height.