Construct Confidence Intervals
Part 1
1. Explain the difference between a 95% confidence interval and a 99% confidence interval in terms of probability
a) To construct a 95% confidence interval for a population, mean µ, what is the correct critical value z*?
A 95% confidence interval implies that in the event that 100 different kinds of samples are taken into consideration and a 95% confidence interval is calculated for every sample, then roughly 95 out of the 100 confidence intervals will have the true mean value, which is µ
To construct a 95% confidence interval for a population, mean µ, the correct critical value of z* is P (-1.96 < Z < 1.96) = 0.95
b) To construct a 99% confidence interval for a population, mean µ, what is the correct critical value z*?
A 99% confidence interval implies that in the event that 100 different kinds of samples are taken into consideration and a 99% confidence interval is calculated for every sample, then roughly 99 out of the 100 confidence intervals will have the true mean value, which is µ
To construct a 99% confidence interval for a population, mean µ, the correct critical value of z* is P (-2.56 < Z < 2.56) = 0.99
2. Explain what the margin of error is and how to calculate it
Margin of error is defined as the range of values both above and below the sample statistics within a confidence interval. Therefore, the margin of error indicates the number of percentage points the outcomes will vary from the real value of the population.
The margin of error can be computed in two ways:
1. Margin of error = Critical value * Standard deviation
2. Margin of error = Critical value * Standard...
References
Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2012). Introduction to probability and statistics. New York: Cengage Learning.
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