Question

A beef rancher randomly sampled 42 cattle from her large herd to obtain a 95% confidence interval to estimate the mean weight of the cows in the herd. The interval obtained was (1010, 1321). If the rancher had used a 90% confidence interval instead, the interval would have been

(A) wider and would have more precision than the original estimate

(B) narrower and would have more precision than the original estimate

(C) wider and would have the same precision as the original estimate

(D) narrower and would have less precision than the original estimate

(E) wider and would have less precision than the original estimate

Answer 1

Answer)

Confidence interval depends on the margin of error

Larger the error wider the interval

Error = z*s.d/√n

Z is for confidence level

As the confidence level increases, z is also increases

So we can say that greater the confidence level greater the error and hence wider the interval

More over we need a wider interval to be more confident that the interval would contain the true population parameter

So answer here is

(D) narrower and would have less precision than the original estimate