Question

A large toiletry distributor claims that 35% of all individuals who purchase toilet paper from the stores that carry its product choose original toilet paper, 28% choose sensitive toilet paper, 20% choose ultra-strong toilet paper, and 17% choose ultra-soft toilet paper. To investigate this claim, researchers collected data from a random sample of customers in a large city. The results were 170 packages of original, 105 sensitive, 80 ultra-strong, and 45 ultra-soft toilet paper purchases. Are the data from the sample consistent with the distributor's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion.

Answer 1

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No, The Data From The Sample Is Not Consistent With The Distributor's Claim.

CLAIM:

Original: 35%

Sensitive: 28%

Ultra-Strong: 20%

Ultra-Soft: 17%

= 35% + 28% + 20% + 17%

= 100%

DATA:

Original: 170 Packs

Sensitive: 105 Packs

Ultra-Strong: 80 Packs

Ultra-Soft: 45 Packs

= 170 Packs + 105 Packs + 80 Packs + 45 Packs

= 400 Packs

Original = 170 ÷ 400 × 100

= 42.5%

Sensitive = 105 ÷ 400 × 100

= 26.25%

Ultra-Strong = 80 ÷ 400 × 100

= 20%

Ultra-Soft = 45 ÷ 400 × 100

= 11.25%

= 42.5% + 26.25% + 20% + 11.25%

= 100%

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