(a) A company is planning to market a new cereal with one of two possible package designs: design A, 5-color without cartoons and design B, 3-color with cartoons. To determine which has the most appeal, seven stores are supplied with all two package designs. All packages are priced the same, so that if any design outsells the others, it will be due primarily to visual attractiveness. The cereal is on the market for several months, and the number of sales for each design at each store is recorded. Design A B Total ΣΣΥ i-1 j-1 (i) (ii) ij 1 111 100 2 102 105 211 207 177,402 Store 4 5 6 7 98 110 129 94 111 105 234 3 120 140 114 127 234 267 192 221 State the assumptions. Perform an appropriate statistical analysis at a = 0.10. Total 810 756 1,566

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(b) The manufacturer of Stay-White toothpaste claims that by the addition of a certain
chemical he can guarantee that over a given period of time, people will have less
dental decay if they clean their teeth regularly with Stay-White, than if they clean
their teeth with ordinary toothpaste. To test this theory, free tubes of Stay-White
were given to 150 children at a school dental clinic, and at the same time, free tubes
of ordinary toothpaste were given to a further 100 children at the clinic. All the
children guaranteed to clean their teeth regularly for 6 months and then return for a
check-up.
At the end of 6 months, it was found that 32 children using Stay-White had dental
decay, whereas 72 children using the ordinary toothpaste had no dental decay.
(i)
(ii)
State the appropriate assumptions.
Do these data provide enough evidence to support the claim? Use α = 0.02.
Transcribed Image Text:(b) The manufacturer of Stay-White toothpaste claims that by the addition of a certain chemical he can guarantee that over a given period of time, people will have less dental decay if they clean their teeth regularly with Stay-White, than if they clean their teeth with ordinary toothpaste. To test this theory, free tubes of Stay-White were given to 150 children at a school dental clinic, and at the same time, free tubes of ordinary toothpaste were given to a further 100 children at the clinic. All the children guaranteed to clean their teeth regularly for 6 months and then return for a check-up. At the end of 6 months, it was found that 32 children using Stay-White had dental decay, whereas 72 children using the ordinary toothpaste had no dental decay. (i) (ii) State the appropriate assumptions. Do these data provide enough evidence to support the claim? Use α = 0.02.
Question 4
(a) A company is planning to market a new cereal with one of two possible package
designs: design A, 5-color without cartoons and design B, 3-color with cartoons. To
determine which has the most appeal, seven stores are supplied with all two package
designs. All packages are priced the same, so that if any design outsells the others, it
will be due primarily to visual attractiveness. The cereal is on the market for several
months, and the number of sales for each design at each store is recorded.
Design
A
B
Total
ΣΣΥ
i-1 j-1
(i)
(ii)
1
111
100
211
2
3
102
120
105 114
207
= 177,402
Store
4
140
127
234 267
5
98
94
192 221
State the assumptions.
Perform an appropriate statistical analysis at a =
6
7
110
129
111 105
234
= 0.10.
Total
810
756
1,566
Transcribed Image Text:Question 4 (a) A company is planning to market a new cereal with one of two possible package designs: design A, 5-color without cartoons and design B, 3-color with cartoons. To determine which has the most appeal, seven stores are supplied with all two package designs. All packages are priced the same, so that if any design outsells the others, it will be due primarily to visual attractiveness. The cereal is on the market for several months, and the number of sales for each design at each store is recorded. Design A B Total ΣΣΥ i-1 j-1 (i) (ii) 1 111 100 211 2 3 102 120 105 114 207 = 177,402 Store 4 140 127 234 267 5 98 94 192 221 State the assumptions. Perform an appropriate statistical analysis at a = 6 7 110 129 111 105 234 = 0.10. Total 810 756 1,566
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