8 Questions
Which of the following best defines the confidence interval for a population mean?
An interval estimate that is likely to contain the population mean
What critical value z_{1-α/2} corresponds to a 95% confidence level?
1.96
If the sample size increases, what happens to the width of the confidence interval?
It decreases
In the formula for a confidence interval, what is represented by σ?
Population standard deviation
What is the value of the standard error if σ = 15 mg/dL and n = 50?
2.13
When constructing a 95% confidence interval for the population mean blood sugar level, what is the margin of error if the sample mean is 120 mg/dL, standard deviation is 15 mg/dL, and sample size is 50?
4.16
For which value of α does z_{1-α/2} equal 2.58?
0.01
What is the interpretation of a 95% confidence interval for the population mean?
Approximately 95% of such intervals will contain the population mean
Study Notes
Confidence Interval for a Population Mean
- A confidence interval for the population mean μ is constructed using the formula: $X ± z_{1-α/2}(\frac{σ}{\sqrt{n}})$
- The formula involves: sample mean X, critical value z_{1-α/2}, population standard deviation σ, and sample size n
- The critical value z_{1-α/2} is determined by the desired level of confidence and is obtained from the standard normal distribution table or calculated using statistical software
Interpreting Confidence Intervals
- A confidence interval provides an interval estimate for μ with a specified level of confidence
- A 95% confidence interval means that approximately 95% of the intervals constructed using this method would contain the true population mean μ
Example: Estimating Average Blood Sugar Level
- Sample mean X = 120 mg/dL, population standard deviation σ = 15 mg/dL, and sample size n = 50
- To construct a 95% confidence interval, the critical value z_{1-α/2} = 1.96 is used
- The 95% confidence interval is calculated as: $120 ± 1.96(\frac{15}{\sqrt{50}})$
Learn how to construct a confidence interval for the population mean using the sample mean, standard deviation, and sample size. Understand the formula and its components.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
