Question

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.

Answer 1

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.