A factory uses a machine to package flour into 5 kg5\text{ kg} bags. The machine is calibrated to fill an average of 5000 g5000\text{ g} with a standard deviation of 8 g8\text{ g}. A random sample of 4040 bags shows a mean of 5003 g5003\text{ g}. The machine must be recalibrated if the sample mean is statistically unusual. Use a significance level of 0.050.05. Should the machine be recalibrated? Explain your reasoning using a hypothesis test.

Yes, because the pp-value is below 0.050.05, indicating the result is statistically significant

No, because the zz-score is not unusual

No, because 50035003 is close to 50005000, and small changes are expected

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1. Intro to Stats and Collecting Data(0)

Intro to Stats
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Levels of Measurement
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Intro to Collecting Data
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Sampling Methods
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2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
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Frequency Distributions
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Histograms
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Bar Graphs and Pareto Charts
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Pie Charts
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Frequency Polygons
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Dot Plots
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Stemplots (Stem-and-Leaf Plots)
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Time-Series Graph
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3. Describing Data Numerically(0)

Mean
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Median
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Mode
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Standard Deviation
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Interpreting Standard Deviation
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Percentiles & Quartiles
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Boxplots
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4. Probability(0)

Basic Concepts of Probability
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Complements
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Addition Rule
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Multiplication Rule: Independent Events
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Introduction to Contingency Tables
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Multiplication Rule: Dependent Events
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Bayes' Theorem
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Fundamental Counting Principle
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Counting
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5. Binomial Distribution & Discrete Random Variables(0)

Discrete Random Variables
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Binomial Distribution
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Poisson Distribution
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Hypergeometric Distribution
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6. Normal Distribution and Continuous Random Variables(0)

Uniform Distribution
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Standard Normal Distribution
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Non-Standard Normal Distribution
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7. Sampling Distributions & Confidence Intervals: Mean(0)

Sampling Distribution of the Sample Mean and Central Limit Theorem
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Introduction to Confidence Intervals
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Confidence Intervals for Population Mean
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Determining the Minimum Sample Size Required
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8. Sampling Distributions & Confidence Intervals: Proportion(0)

Sampling Distribution of Sample Proportion
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Confidence Intervals for Population Proportion
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Chi Square Distribution
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Confidence Intervals for Population Variance
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9. Hypothesis Testing for One Sample(0)

Steps in Hypothesis Testing
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Performing Hypothesis Tests: Means
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Performing Hypothesis Tests: Proportions
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Performing Hypothesis Tests: Variance
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Critical Values and Rejection Regions
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Link Between Confidence Intervals and Hypothesis Testing
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Type I & Type II Errors
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10. Hypothesis Testing for Two Samples(0)

Two Proportions
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Two Means - Unknown, Unequal Variance
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Two Means - Unknown, Equal Variance
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Two Means - Known Variance
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Two Means - Matched Pairs (Dependent Samples)
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Two Variances and F Distribution
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11. Correlation(0)

Scatterplots & Intro to Correlation
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Correlation Coefficient
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12. Regression(0)

Linear Regression & Least Squares Method
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Coefficient of Determination
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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
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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
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9. Hypothesis Testing for One Sample

Performing Hypothesis Tests: Means

9. Hypothesis Testing for One Sample

Performing Hypothesis Tests: Means: Videos & Practice Problems

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Problem 2Multiple Choice

A factory uses a machine to package flour into $5 kg$ bags. The machine is calibrated to fill an average of $5000 g$ with a standard deviation of $8 g$ . A random sample of $40$ bags shows a mean of $5003 g$ . The machine must be recalibrated if the sample mean is statistically unusual. Use a significance level of $0.05$ . Should the machine be recalibrated? Explain your reasoning using a hypothesis test.

No, because the $z$ -score is not unusual

No, because $5003$ is close to $5000$ , and small changes are expected

Yes, because the $p$ -value is below $0.05$ , indicating the result is statistically significant

Yes, because the sample mean is slightly above the claimed mean

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