Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

Statistics

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

Previous problemNext problem

1:47 minutes

Problem 6.1.13

Textbook Question

In Exercises 13–16, find the margin of error for the values of c, σ and n.
c = 0.95, σ = 5.2, n = 30

Verified step by step guidance

Step 1: Understand the formula for the margin of error (ME). The formula is: ME = z * (σ / √n), where z is the critical value corresponding to the confidence level (c), σ is the population standard deviation, and n is the sample size.

Step 2: Determine the critical value (z) for the given confidence level (c = 0.95). For a 95% confidence level, the z-value can be found using a z-table or standard normal distribution. It is approximately 1.96.

Step 3: Plug in the given values into the formula. Here, σ = 5.2 and n = 30. The formula becomes: ME = 1.96 * (5.2 / √30).

Step 4: Simplify the denominator by calculating the square root of the sample size (n). Compute √30.

Step 5: Divide the population standard deviation (σ = 5.2) by the square root of the sample size (√30), then multiply the result by the critical value (z = 1.96) to find the margin of error.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Margin of Error

The margin of error quantifies the uncertainty in a sample estimate. It indicates the range within which the true population parameter is expected to lie, given a certain confidence level. A smaller margin of error suggests a more precise estimate, while a larger margin indicates more variability in the data.

Confidence Level (c)

The confidence level represents the probability that the margin of error will contain the true population parameter. A confidence level of 0.95, for example, means that if the same sampling procedure were repeated multiple times, approximately 95% of the calculated margins of error would capture the true parameter.

Standard Deviation (σ) and Sample Size (n)

Standard deviation (σ) measures the dispersion of data points around the mean, indicating how spread out the values are. The sample size (n) refers to the number of observations in the sample. Both σ and n are critical in calculating the margin of error, as they influence the precision of the estimate; larger samples generally yield smaller margins of error.

Watch next

Master Population Standard Deviation Known with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.

c = 0.80

views

Textbook Question

In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.

c = 0.97

views

Textbook Question

Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.

views

Textbook Question

Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.

views

Textbook Question

In Exercises 13–16, find the margin of error for the values of c, σ and n.

c = 0.975, σ = 4.6, n = 100

views

Textbook Question

Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.

c = 0.88

views

Textbook Question

In Exercises 21–24, construct the indicated confidence interval for the population mean μ.

c = 0.95, xbar = 31.39, σ = 0.80, n = 82.

views

Textbook Question

In Exercises 21–24, construct the indicated confidence interval for the population mean μ.

c = 0.80, xbar = 20.6, σ = 4.7, n = 100.

views

Show more practices