A random sample of dogs was checked to see how many wore a collar. The 95% confi

Question

A random sample of dogs was checked to see how many wore a collar. The 95% confidence interval for the percentage of all dogs that wear a collar turned out to be 0.82 to 0.96. Which of these is not a true statement.

A. You can reject the hypothesis that 75% of all dogs wear a collar.

B. You cannot reject the hypothesis that 90% of all dogs wear a collar.

C. If 90% of all dogs wear a collar, then you are reasonably likely to get a result like the one from this sample.

D. If 75% of all dogs wear a collar, then you are reasonably likely to get a result like the one from this sample.

E. The true proportion of dogs that wear a collar may or may not be between .82 and .96.

Explanation / Answer

Option D is not true.

A) 0.75 is not in the interval. So we can reject the hypotheisis. So A is correct.

B) 0.90 is in the interval. So we cannot reject the hypotheisis. So B is also correct.

C) C is also correct.

D) 0.75 is not in the interval. So it is not likely to get a result like the one from the population.So D is wrong

E) Also correct .

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