A researcher claims that the mean weight of apples in a storage bin is 180180 grams. To test this claim, a quality control officer collects a random sample of 1212 apples, and records their weights (in grams) as:178,182,175,180,176,179,181,183,177,179,180,178 178, 182, 175, 180, 176, 179, 181, 183, 177, 179, 180, 178Assuming that the weights are normally distributed, and the sample standard deviation is approximately 2.382.38 grams, determine whether there is enough evidence at the 0.050.05 significance level to reject the researcher’s claim that the mean weight is 180180 grams.

Reject H0H_0; the mean is definitely greater than 180 g180\text{ g}

Fail to reject H0H_0; this proves the mean is exactly 180 g180\text{ g}

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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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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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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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Goodness of Fit Test
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Multiple Comparisons: Tukey-Kramer 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 20Multiple Choice

A researcher claims that the mean weight of apples in a storage bin is $180$ grams. To test this claim, a quality control officer collects a random sample of $12$ apples, and records their weights (in grams) as:
$178 comma 182 comma 175 comma 180 comma 176 comma 179 comma 181 comma 183 comma 177 comma 179 comma 180 comma 178$
Assuming that the weights are normally distributed, and the sample standard deviation is approximately $2.38$ grams, determine whether there is enough evidence at the $0.05$ significance level to reject the researcher’s claim that the mean weight is $180$ grams.

Fail to reject $H sub 0$ ; there is not enough evidence to show the mean is different from $180 g$

Reject $H sub 0$ ; the mean is definitely greater than $180 g$

Reject $H sub 0$ ; there is strong evidence the mean is different from $180 g$

Fail to reject $H sub 0$ ; this proves the mean is exactly $180 g$

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