104k views
5 votes
A veterinarian sampled 235 sheep from a large herd to obtain a 90% confidence interval for the mean weight of wool from the sheep. The interval was (23.7 lbs., 33.6 lbs.). If the veterinarian had used a 95% confidence interval instead, the confidence interval would be:_____.A. Wider and would have a smaller chance of missing the true mean. B. Narrower and would have a larger chance of missing the true mean. C. Narrower and would have a smaller chance of missing the true mean. D. Wider and would have a larger chance of missing the true mean. E. Wider but the chance of missing the true mean cannot be determined.

User Daspilker
by
8.4k points

1 Answer

1 vote

Answer:

A. Wider and would have a smaller chance of missing the true mean.

Explanation:

Margin of error for a confidence interval:

The margin of error for a confidence interval is given by:


M = z(\sigma)/(√(n))

In which z is related to the confidence level(the higher the confidence level, the higher the value of z),
\sigma is the standard deviation of the population and n is the size of the sample.

95% confidence interval

Would be wider than the 90% confidence interval, due to the higher value of z.

Also, a x% confidence interval has a x% chance of having the true mean, and a (100-x)% probability of missing the true mean.

Then, a 95% confidence interval has a smaller(5%) chance of missing the true mean compared to the 90% confidence interval(10%). This means that the correct answer is given by option A.

User Lightandlight
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.