An advertiser claims that 9 out of 10 dentists (90%) recommend Brand X toothpaste. A consumer group investigates the truth of this claim.

Question

They survey a randomly selected sample of 500 dentists, and find that 444 of them recommend Brand X toothpaste.

Based on this survey, they construct a 95% confidence interval for the proportion of dentists that recommend Brand X toothpaste of (0.860,0.916).

What can be concluded from this survey?
There is statistically significant evidence that 90% of dentists recommend Brand X toothpaste.
There is statistically significant evidence that the proportion of dentists that recommend Brand X toothpaste is less than 90%.
There is statistically significant evidence that the proportion of dentists that recommend Brand X toothpaste is greater than 90%.
There is no statistically significant evidence that the proportion of dentists that recommend Brand X toothpaste is different from 90%.
Nothing can be concluded from this sample.

Answer 1

From this survey, it can be concluded that there is no statistically significant evidence that the proportion of dentists that recommend Brand X toothpaste is different from 90%. This is because the 95% confidence interval for the proportion of dentists recommending Brand X toothpaste includes the claimed rate of 90%.