Question

The data in Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag.

Construct a 95% confidence interval for the true mean number of colors on national flags.

Using the same $\overline{x}$ , $s_x$ , and n = 39, how would the error bound change if the confidence level were reduced to 90%? Why?

Short answer

The error bound will be smaller.

Step-by-step solution

Given information

Given in the question that

$X=$the number of colors on a national flag

Solution

Error bound

The Lagrange error bound of a Taylor polynomial shows the worst-case method for the distinction between the assessed value of the procedure as delivered by the Taylor polynomial and the actual value of the function.

Here the confidence level is reduced to $90\%$

The sample mean, sample size, and sample standard deviation are the same.

So the formula is,

$EBM=t_{n-1}\left(\frac{\alpha }{2}\right)\frac{s}{\sqrt{n}}$

The error bound decreases if the confidence level decreases because the confidence level decreases the area under the curve to capture the true population mean is less.