A coffee shop's automated machine dispenses an amount of liquid that follows a uniform distribution between 11.511.5 ounces and 12.512.5 ounces. The population mean is 12.012.0 ounces, and the population standard deviation is 0.290.29 ounces. If the coffee shop takes a random sample of 100100 cups and calculates the sample mean liquid amount (xˉ\bar{x}), which of the following statements about the sampling distribution of xˉ\bar{x} is true?

The distribution is uniform between 11.511.5 and 12.512.5 ounces, since a sample mean must reflect the population's original shape

The mean of the sampling distribution will be 0.50.5 ounces

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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
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Residuals
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Coefficient of Determination
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Inferences for Slope
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Prediction Intervals
(0)

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

Goodness of Fit Test
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Contingency Tables
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Independence Tests
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Homogeneity Tests
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14. ANOVA(0)

Introduction to ANOVA
(0)

Multiple Comparisons: Tukey Test
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Multiple Comparisons: Tukey-Kramer Test
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Multiple Comparisons: Bonferoni Test
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Two-Way ANOVA
(0)

7. Sampling Distributions & Confidence Intervals: Mean

Sampling Distribution of the Sample Mean and Central Limit Theorem

7. Sampling Distributions & Confidence Intervals: Mean

Sampling Distribution of the Sample Mean and Central Limit Theorem: Videos & Practice Problems

Video Lessons Practice Worksheet

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Problem 52Multiple Choice

A coffee shop's automated machine dispenses an amount of liquid that follows a uniform distribution between $11.5$ ounces and $12.5$ ounces. The population mean is $12.0$ ounces, and the population standard deviation is $0.29$ ounces. If the coffee shop takes a random sample of $100$ cups and calculates the sample mean liquid amount ( $\overset{ˉ}{x}$ ), which of the following statements about the sampling distribution of $\overset{ˉ}{x}$ is true?

The distribution is uniform between $11.5$ and $12.5$ ounces, since a sample mean must reflect the population's original shape

The mean of the sampling distribution will be $0.5$ ounces

The distribution will be approximately normal with a standard error of $0.029$ ounces

The distribution will be exactly normal because the sample size is greater than $30$

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