You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
Find the critical value that corresponds to a confidence level of 98%.
(Report answer accurate to three decimal places with appropriate rounding.)
98% = mean ± 2.33 SEm
SEm = SD/√n
To find the critical value that corresponds to a confidence level of 98%, we need to use the standard normal distribution table or a statistical calculator.
Step 1: Recall that the confidence level corresponds to the area under the normal curve. In this case, we want a confidence level of 98%, which means we are looking for the area to the left of the critical value.
Step 2: Subtract the confidence level from 1 to find the area to the left of the critical value.
1 - 0.98 = 0.02
Step 3: Divide this remaining area by 2 because we want to find the area in the tails of the distribution (i.e., both ends of the curve).
0.02 / 2 = 0.01
Step 4: Look up the z-value that corresponds to an area of 0.01 in the normal distribution table or use a statistical calculator. The z-value represents the number of standard deviations from the mean.
Using the normal distribution table or a calculator, we find that the z-value for an area of 0.01 is approximately 2.326.
So, the critical value that corresponds to a confidence level of 98% is approximately 2.326 (accurate to three decimal places with appropriate rounding).