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? Use a significance level of 1%.  

1. To test: H_o: (Click to select)pαβμx¯ =   vs. H_a: (Click to select) x¯μ β αp (Click to select)><=≥≤≠

2. Test Statistic (Round to 3 decimals): z =

3. p-value (Round to 3 decimals):

Conclusion: At α = , (Click to select)reject Hado not reject Hareject Hodo not reject Ho since p-value (Click to select)><= α. We have (Click to select)sufficientinsufficient evidence to conclude that the (Click to select)sample meansample variancesample proportionpopulation meanpopulation variancepopulation proportion of dentists who recommend the ingredients in the manufacturer's toothpaste (Click to select)is less thanis greater thanis equal todiffers from .

Therefore, there (Click to select)is notis enough evidence to conclude that more than four out of five dentists recommend the ingredients in the manufacturer's toothpaste.  

Answer 1

Solution:

Given:

Sample size = n = 400

x = number of respondents responded that they would recommend the ingredients in the manufacturer's toothpaste= 334

Claim: more than four out of five dentists recommend the ingredients in its product.

that is: p > 4/5

that is: p > 0.8

Level of significance =

Step 1) State H0 and Ha:

H0: p = 0.8

Vs

Ha: p > 0.8

Step 2) Find test statistic value:

thus

Step 3) P-value:

P-value = P( Z> 1.750)

P-value = 1 - P( Z< 1.750)

Look in z table for z = 1.7 and 0.05 and find area.

From z table we get: P( Z< 1.75) = 0.9599

Thus

P-value = 1 - P( Z< 1.750)

P-value = 1 - 0.9599

P-value = 0.0401

P-value = 0.040

Step 4) Conclusion:

At , do not reject H0, since p-value > . We have insufficient evidence to conclude that the population proportion of dentists who recommend the ingredients in the manufacturer's toothpaste greater than 0.8.
Therefore, there is not enough evidence to conclude that more than four out of five dentists recommend the ingredients in the manufacturer's toothpaste.