Question

In: Statistics and Probability

06. Testing a new insect repellent. (Adapted from McClave, Benson, & Sincich, 12th edition, page 556)....

06. Testing a new insect repellent. (Adapted from McClave, Benson, & Sincich, 12th edition, page 556). A study in the Journal of the American Mosquito Control Association (Mar. 1995) investigated whether a tent sprayed with a commercially available 1% permethrin formulation would protest people, both inside and outside the tent, against biting mosquitoes. Two canvas tents — one treated with permethrin, the other untreated — were position 25 meters apart on flat, dry ground in an area infested with mosquitoes. Eight people participated in the experiment, with four randomly assigned to each tent. Of the four stationed at each tent, two were randomly assigned to stay inside the tent (at opposite corners) and two to stay outside the tent (at opposite corners). During a specified 20-minute period during the night, each person kept count of the number of mosquito bites received. The goal of the study was to determine the effect of both Tent type (treated or untreated) and the Location (inside and outside) on the mean mosquito bite count.

The data for the study are shown in the table below. The summary values for the factors are given with A = Tent type and B = Location.

Inside Outside
Treated

4

7

8

11
Untreated

6

10

24

16

A1=30, A2=56, B1=27, B2=59, AB11= 11, AB12= 19, A21=16, AB22= 40

CM=924.5

Fill this table out

Source df SS MS F
Treatments
Tent Type
Location
Tent Type*Location
Error
Total

These are the correct answers, but I don't understand how we got this.

Source df SS MS F
Treatments 3 244.5 81.5 6.8980
Tent Type 1 84.5 84.5 10.4490
Location 1 128 128 2.6122
Tent Type*Location 1 32 32
Error 4 49 12.25
Total 7 293.5

Solutions

Expert Solution

copy paste the data in excel

inside outside
treated 4 8
7 11
untreated 6 24
10 16

go to data -> data analysis -> anova two with replication

rows per sample = 2

Anova: Two-Factor With Replication
SUMMARY inside outside Total
treated
Count 2 2 4
Sum 11 19 30
Average 5.5 9.5 7.5
Variance 4.5 4.5 8.333333333
untreated
Count 2 2 4
Sum 16 40 56
Average 8 20 14
Variance 8 32 61.33333333
Total
Count 4 4
Sum 27 59
Average 6.75 14.75
Variance 6.25 48.91667
ANOVA
Source of Variation SS df MS F P-value
Sample 84.5 1 84.5 6.897959184 0.058406303
Columns 128 1 128 10.44897959 0.031900188
Interaction 32 1 32 2.612244898 0.181346882
Within 49 4 12.25
Total 293.5 7

orchestra answered 1 year ago
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