Question

Determine if the following statements are true or false, and explain your reasoning. If false, state how it could be corrected. (a) If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval. true false

Answer 1

Answer:

True

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

$M = z\frac{s}{\sqrt{n}}$

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

A higher confidence level leads to a larger margin of error, that is, a wider interval. The interval expands around it's lower and upper bounds, which means that if a value is part of a lower confidence interval(such as 95%), it will be part of the higher(such as 99%), and the answer to this question is true.