Question

(b) find the 90% confidence interval of the mean of these pounds. round intermediate answers to at least three decimal places. round your final answers to one decimal place.
28.1 < μ < 29.9
part 3 of 4
(c) find the 95% confidence interval of the mean of these pounds. round intermediate answers to at least three decimal places. round your final answers to one decimal place.
27.9 < μ < 30.1
part: 3 / 4
part 4 of 4
(d) which interval is larger? why?
the % confidence interval is larger. an interval with a range of values than the % confidence interval will be more likely to contain the true population mean.

Explanation:

As the confidence level increases, the critical value (e.g., \(z\)-score or \(t\)-score depending on the situation) increases. A higher critical value leads to a larger margin of error (\(E = z\times\frac{\sigma}{\sqrt{n}}\) or \(E = t\times\frac{s}{\sqrt{n}}\)). Since \(95\%>90\%\), the \(95\%\) confidence interval has a larger margin of error, making the interval wider. A wider interval (larger range of values) has a higher probability of capturing the true population mean because it covers more potential values of the parameter.

Answer:

The \(95\%\) confidence interval is larger. An interval with a larger range of values than the \(90\%\) confidence interval will be more likely to contain the true population mean.