Question

In a television commercial, the manufacturer of a toothpaste claims that more than four out of five dentists recommend the ingredients in its product. To test that claim, a consumer-protection group randomly sampled 400 dentists and asked each dentist whether they would recommend the ingredients in the manufacturer's toothpaste. 334 of the 400 dentists responded that they would recommend the ingredients in the manufacturer's toothpaste. Can the consumer-protection group conclude that the manufacturer's claim is true

Answer 1

Based on the sample of 400 dentists, with 334 recommending the toothpaste, the claim that more than four out of five dentists recommend the toothpaste's ingredients is supported, as 83.5% translates to more than four out of five.

Step-by-step explanation:

The student asked if the consumer-protection group can conclude that the manufacturer's claim that more than four out of five dentists recommend the ingredients in its toothpaste is true, based on a sample of 400 dentists where 334 confirmed their recommendation. To evaluate the claim, we perform a simple calculation to find the proportion of dentists in the sample who recommend the toothpaste:

Proportion of recommendations = Number of positive responses / Total number of responses = 334 / 400 = 0.835

This means that 83.5% of the sampled dentists recommend the toothpaste, which translates to more than four out of five dentists (80%). Assuming the sample is properly randomized and representative of the entire population of dentists, the consumer-protection group can conclude the manufacturer's claim is supported by this sample.

Answer 2

Following are the responses to the given question:

Step-by-step explanation:

n = 400

x = amount of displaying the reacts which would allow the fixing in the producing toothpaste = 334

Its value is more than
`(4)/(5)` dentists suggest the ingredient of the product.

`\to p > (4)/(5)\\\\\to p > 0.8\\\\`

Level of significance =
`\alpha =0.01`