Question

The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% confidence interval, a 99% confidence interval will be:__________(a) narrower and would involve a larger risk of being incorrect.
(b) wider and would involve a smaller risk of being incorrect.
(c) narrower and would involve a smaller risk of being incorrect.
(d) wider and would involve a larger risk of being incorrect.

Answer 1

Answer:

Option (a) narrower and would involve a larger risk of being incorrect.          

Step-by-step explanation:

We have to compare a 95% confidence interval to a 99% confidence interval.

• For a 95% confidence interval and 99% confidence interval, confidence level is lower for 95% confidence interval.
• With a lower confidence level, there would be less margin of error.
• Thus, 95% confidence interval is narrower as compared to the 99% confidence interval.
• Since, a 95% interval is narrower there are less values included in the interval that could give right estimate for the parameter.

Thus, we can write,

Compared to a 95% confidence interval, a 99% confidence interval will be Option (a) narrower and would involve a larger risk of being incorrect.