Question

The following questions require that you conduct appropriate tests of the null hypotheses outlined in each question using an a=0.05 significance level. In all cases you are expected to use the appropriate inferential statistical test available in the Excel data analysis tool pack. Questions requiring a post hoc means comparison test (ie Scheffe’s or Tukey’s HSD test) are worth 20 marks, otherwise they are worth 10 marks.

A toxicologist has conducted a study to determine whether a new insecticide will reduce the fecundity (number of eggs per day) of lady bird beetles, a beneficial non-target insect. Test the null hypothesis that there is no difference in the fecundity of the beetles in the three experimental treatments. If necessary, complete a means comparison test (i.e. Scheffé's test).

Control	Low Dose	High Dose
16	21	29
22	27	33
15	18	21
23	26	22
30	30	27
20	24	34
23	29	24

Answer 1

Control	Low Dose	High Dose
16	21	29
22	27	33
15	18	21
23	26	22
30	30	27
20	24	34
23	29	24

H₀: or there is no difference in the fecundity of the beetles in the three experimental treatments

H₁: Atleast two groups are different.

Goto excel-->enter data-->data-->data analysis-->Anova:Single factor:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	7	149	21.28571429	25.2380952
Column 2	7	175	25	18.6666667
Column 3	7	190	27.14285714	26.4761905
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	122.952381	2	61.47619048	2.62043302	0.10027249	3.554557146
Within Groups	422.2857143	18	23.46031746
Total	545.2380952	20

F_cal=2.62043302

F_critical=3.554557146

p-value=0.10027249

F_cal < F_critical also p-value=0.10027249 >0.05 hence we accept the null hypothesis or there is no difference in the fecundity of the beetles in the three experimental treatments.

post hoc means comparison test (ie Scheffe’s or Tukey’s HSD test):

We calculate t_{group1,group2}= | | >MSE the difference is significant.

Groups	Average
Column 1	21.28571429
Column 2	25
Column 3	27.14285714

MSE=23.46031746

t_{control,low dose}= <MSE( insignificant)

p-value=0.3454023>0.05(insignificant).

t_{low dose,high dose}= <MSE(insignificant)

p-value=0.0874468>0.05(insignificant).

t_{high dose,control}= <MSE(insignificant)

p-value=0.6808151>0.05(insignificant).

Hence, there is no significant difference between the populations.

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