A quality‐control engineer has data on the weights of 120120 jellybeans from a production batch; the true mean weight of all 120120 candies is known to be 0.9820.982 g. To re‐estimate the mean without using all data, she isolates the 4040 green jellybeans and computes a sample mean of x‾=0.985\overline{x}=0.985 g and a sample standard deviation of s=0.020s=0.020 g. Treat these 4040 as a simple random sample from the population of 120120. Construct a 95%95\% confidence interval for the true mean weight, applying the finite‐population correction factor. Finally, compare your interval to the known mean of 0.9820.982 g.

0.9800.980 g μ0.990 g; the known mean lies well within the interval.

Table of contents

Prepare for your exams

Upload your syllabus and get recommendations on what to study and when. No syllabus? Sharing your exam schedule works too.

Skip topic navigation

1. Intro to Stats and Collecting Data(0)

Intro to Stats
(0)

Levels of Measurement
(0)

Intro to Collecting Data
(0)

Sampling Methods
(0)

2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
(0)

Frequency Distributions
(0)

Histograms
(0)

Bar Graphs and Pareto Charts
(0)

Pie Charts
(0)

Frequency Polygons
(0)

Dot Plots
(0)

Stemplots (Stem-and-Leaf Plots)
(0)

Time-Series Graph
(0)

3. Describing Data Numerically(0)

Mean
(0)

Median
(0)

Mode
(0)

Standard Deviation
(0)

Interpreting Standard Deviation
(0)

Percentiles & Quartiles
(0)

Boxplots
(0)

4. Probability(0)

Basic Concepts of Probability
(0)

Complements
(0)

Addition Rule
(0)

Multiplication Rule: Independent Events
(0)

Introduction to Contingency Tables
(0)

Multiplication Rule: Dependent Events
(0)

Bayes' Theorem
(0)

Fundamental Counting Principle
(0)

Counting
(0)

5. Binomial Distribution & Discrete Random Variables(0)

Discrete Random Variables
(0)

Binomial Distribution
(0)

Poisson Distribution
(0)

Hypergeometric Distribution
(0)

6. Normal Distribution and Continuous Random Variables(0)

Uniform Distribution
(0)

Standard Normal Distribution
(0)

Non-Standard Normal Distribution
(0)

7. Sampling Distributions & Confidence Intervals: Mean(0)

Sampling Distribution of the Sample Mean and Central Limit Theorem
(0)

Introduction to Confidence Intervals
(0)

Confidence Intervals for Population Mean
(0)

Determining the Minimum Sample Size Required
(0)

8. Sampling Distributions & Confidence Intervals: Proportion(0)

Sampling Distribution of Sample Proportion
(0)

Confidence Intervals for Population Proportion
(0)

Chi Square Distribution
(0)

Confidence Intervals for Population Variance
(0)

9. Hypothesis Testing for One Sample(0)

Steps in Hypothesis Testing
(0)

Performing Hypothesis Tests: Means
(0)

Performing Hypothesis Tests: Proportions
(0)

Performing Hypothesis Tests: Variance
(0)

Critical Values and Rejection Regions
(0)

Link Between Confidence Intervals and Hypothesis Testing
(0)

Type I & Type II Errors
(0)

10. Hypothesis Testing for Two Samples(0)

Two Proportions
(0)

Two Means - Unknown, Unequal Variance
(0)

Two Means - Unknown, Equal Variance
(0)

Two Means - Known Variance
(0)

Two Means - Matched Pairs (Dependent Samples)
(0)

Two Variances and F Distribution
(0)

11. Correlation(0)

Scatterplots & Intro to Correlation
(0)

Correlation Coefficient
(0)

12. Regression(0)

Linear Regression & Least Squares Method
(0)

Residuals
(0)

Coefficient of Determination
(0)

Inferences for Slope
(0)

Prediction Intervals
(0)

Quadratic Regression
(0)

13. Chi-Square Tests & Goodness of Fit(0)

Goodness of Fit Test
(0)

Contingency Tables
(0)

Independence Tests
(0)

Homogeneity Tests
(0)

14. ANOVA(0)

Introduction to ANOVA
(0)

Multiple Comparisons: Tukey Test
(0)

Multiple Comparisons: Tukey-Kramer Test
(0)

Multiple Comparisons: Bonferoni Test
(0)

Two-Way ANOVA
(0)

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean

7. Sampling Distributions & Confidence Intervals: Mean

Confidence Intervals for Population Mean: Videos & Practice Problems

Video Lessons Practice Worksheet

Back to all problems

36 of 0

PreviousNext

Problem 36Multiple Choice

A quality‐control engineer has data on the weights of $120$ jellybeans from a production batch; the true mean weight of all $120$ candies is known to be $0.982$ g. To re‐estimate the mean without using all data, she isolates the $40$ green jellybeans and computes a sample mean of $x overline equals 0.985$ g and a sample standard deviation of $s equals 0.020$ g. Treat these $40$ as a simple random sample from the population of $120$ . Construct a $95 percent sign$ confidence interval for the true mean weight, applying the finite‐population correction factor. Finally, compare your interval to the known mean of $0.982$ g.

$0.982$ g $is less than mu is less than 0.995$ g; the known mean lies exactly at the lower bound of the interval.

$0.980$ g $is less than mu is less than 0.990$ g; the known mean lies well within the interval.

$0.977$ g $is less than mu is less than 0.982$ g; the known mean lies exactly at the upper bound of the interval.

$0.990$ g $is less than mu is less than 1.000$ g; the known mean lies below the interval, indicating the sample overestimates the true mean.

0 Comments

Download the Mobile app

Accessibility

Privacy

Do not sell my personal information