A factory manager claims that the average daily output of machines is greater than 200200 units. To test this claim, a random sample of 3030 machines shows a mean output of 206206 units per day. The population standard deviation is known to be 1212 units. At the 0.100.10 level of significance, is there sufficient evidence to support the manager’s claim?

A tt-test should be used instead of a zz-test since the sample size is small.

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1. Introduction to Statistics(0)

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

Linear Regression & Least Squares Method
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Goodness of Fit Test
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Contingency Tables
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Homogeneity Tests
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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 29Multiple Choice

A factory manager claims that the average daily output of machines is greater than $200$ units. To test this claim, a random sample of $30$ machines shows a mean output of $206$ units per day. The population standard deviation is known to be $12$ units. At the $0.10$ level of significance, is there sufficient evidence to support the manager’s claim?

A $t$ -test should be used instead of a $z$ -test since the sample size is small.

There is insufficient evidence to support the claim that the average output is more than $200$ units.

There is sufficient evidence to conclude that the average output is less than $200$ units.

There is sufficient evidence to support the claim that the average output is more than $200$ units.

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