Question
An advertiser claims that 9 out of 10 dentists (90%) recommend Brand X toothpaste. A consumer group investigates the truth of this claim.
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.
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.
Answers
GPT 3.5
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%.