One Tailed and Two Tailed Tests, Critical Values, & Significance Level - Inferential Statistics

The Organic Chemistry Tutor
2 Oct 201905:41
EducationalLearning
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TLDRThis educational video delves into the distinctions between one-tailed and two-tailed tests in hypothesis testing, using a practical example of a company's potato chip bag weights. It explains that the choice between a one-tailed or two-tailed test hinges on the alternative hypothesis. A two-tailed test is used when the hypothesis does not equal a specific value, indicating potential differences in both directions. Conversely, one-tailed tests target specific directions: a left-tailed test for means less than a certain value, and a right-tailed test for means greater than it. The video also covers key concepts like null hypothesis, critical values, significance levels, and how to interpret Z values to make decisions about hypotheses.

Takeaways
  • ๐Ÿ“ The choice between a one-tailed and a two-tailed test depends on the alternative hypothesis.
  • ๐Ÿ“ˆ A two-tailed test is used when the alternative hypothesis suggests a mean is not equal to a certain value.
  • ๐Ÿ“Š In a two-tailed test, rejection regions are on both sides of the distribution, indicating areas where the null hypothesis is rejected.
  • ๐Ÿ“– Critical values separate the rejection regions from the fail-to-reject region in the distribution.
  • ๐Ÿ”ฌ The significance level (alpha) is split between two tails in a two-tailed test, each tail having an area of alpha/2.
  • ๐Ÿ“‰ To decide on rejecting or not rejecting the null hypothesis, compare the calculated z value to the critical value.
  • ๐Ÿ“— One-tailed tests are divided into left-tailed and right-tailed, based on the direction of the alternative hypothesis.
  • ๐Ÿ”ฅ A left-tailed test is appropriate when the alternative hypothesis suggests the mean is less than a specific number.
  • ๐Ÿ’ก A right-tailed test is used when the alternative hypothesis indicates the mean is greater than a certain value.
  • ๐Ÿ“š The significance level remains the same (0.05) for both one-tailed and two-tailed tests at a 95% confidence level.
Q & A

  • What is the null hypothesis in the potato chip bag mass example?

    -The null hypothesis is that the average mass of each potato chip bag is 100 grams.

  • What does the alternative hypothesis propose in the potato chip example?

    -The alternative hypothesis proposes that the mean mass of the potato chip bags is not 100 grams.

  • When is a two-tailed test used in hypothesis testing?

    -A two-tailed test is used when the alternative hypothesis specifies that a parameter does not equal a certain value, indicating the possibility of variation in two directions from the null hypothesis.

  • What do the shaded areas in a two-tailed test represent?

    -In a two-tailed test, the shaded areas on both ends of the normal distribution curve represent the rejection regions, where the null hypothesis would be rejected.

  • What are critical values in the context of hypothesis testing?

    -Critical values are the z values that separate the rejection regions from the fail to reject region in a hypothesis test, marking the thresholds for deciding whether to reject the null hypothesis.

  • How is the significance level (alpha) related to the confidence level?

    -The significance level (alpha) is the complement of the confidence level, such that alpha = 1 - confidence level. For a 95% confidence level, alpha would be 0.05.

  • What determines whether the null hypothesis should be rejected or not?

    -The decision to reject or not reject the null hypothesis is based on whether the calculated test statistic (e.g., z value) exceeds the critical value(s), placing it within the rejection region.

  • What is the difference between one-tailed and two-tailed tests in hypothesis testing?

    -One-tailed tests are used when the alternative hypothesis specifies a direction (less than or greater than), while two-tailed tests are used when the alternative hypothesis indicates a parameter does not equal a certain value, suggesting possible differences in both directions.

  • When should a left-tailed test be used?

    -A left-tailed test should be used when the alternative hypothesis suggests that the parameter of interest is less than a certain value.

  • When is a right-tailed test appropriate in hypothesis testing?

    -A right-tailed test is appropriate when the alternative hypothesis suggests that the parameter of interest is greater than a certain value.

Outlines
00:00
๐Ÿ“ˆ How to Determine When to Use One-Tailed vs Two-Tailed Tests

This paragraph explains how to determine when to use a one-tailed test versus a two-tailed test when solving hypothesis testing problems. It provides an example of a potato chip company where the null hypothesis is a mean bag weight of 100g. A two-tailed test is used when the alternative hypothesis does not equal a value. One-tailed tests are used when the alternative hypothesis states the mean is less than or greater than a value.

05:00
๐Ÿ˜ฒ Visualizing the Rejection Regions for Different Test Types

This paragraph further visualizes rejection regions for two-tailed, left-tailed, and right-tailed tests. It explains how to calculate z-values, compare them to critical values, and determine whether to reject the null hypothesis based on where the z-value falls on the distribution.

Mindmap
Keywords
๐Ÿ’กHypothesis Testing
Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. In the video, it is the central theme as it discusses how to decide between using a one-tailed or two-tailed test based on the hypothesis. The example given involves testing whether the average mass of potato chip bags differs from a known value, highlighting the process of comparing a null hypothesis against an alternative hypothesis to make statistical inferences.
๐Ÿ’กNull Hypothesis
The null hypothesis, often denoted as H0, is a statement that indicates no effect or no difference, serving as a default assumption to be tested against an alternative hypothesis. In the video, the null hypothesis is that the average mass of each potato chip bag is 100 grams. It represents the hypothesis that the study seeks to evidence against or fail to reject based on the data.
๐Ÿ’กAlternative Hypothesis
The alternative hypothesis, denoted as Ha, is a statement that suggests a new or different effect, directly challenging the null hypothesis. In the video, an employee believes that the average mass of potato chip bags is not 100 grams, which becomes the alternative hypothesis. This hypothesis drives the choice between a one-tailed and two-tailed test, depending on whether the difference is specified as less than, greater than, or not equal to a certain value.
๐Ÿ’กTwo-tailed Test
A two-tailed test is used when the alternative hypothesis specifies that a parameter is not equal to a certain value, without directionality. The video explains that when the alternative hypothesis suggests the mean is not equal to 100 grams, a two-tailed test is appropriate. This involves checking for statistical significance in both tails of the distribution, reflecting the possibility of the parameter being either less than or greater than the null hypothesis value.
๐Ÿ’กOne-tailed Test
A one-tailed test is chosen when the alternative hypothesis specifies a direction, stating that a parameter is either less than or greater than a certain value. The video describes two scenarios: a left-tailed test if the mean is expected to be less than 100 grams and a right-tailed test if the mean is expected to be greater than 100 grams. This focuses the hypothesis testing on one direction, increasing the test's power to detect an effect in that direction.
๐Ÿ’กSignificance Level (Alpha)
The significance level, denoted as alpha, is the probability of rejecting the null hypothesis when it is true, essentially measuring the risk of a Type I error. The video sets alpha at 0.05, meaning there's a 5% risk of incorrectly rejecting the null hypothesis. In a two-tailed test, this alpha is split between the two tails of the distribution, guiding the determination of critical values and decision boundaries.
๐Ÿ’กCritical Values
Critical values are threshold values that define the boundaries of the rejection regions in hypothesis testing. The video explains that these values separate the area under the distribution curve into regions where the null hypothesis is either rejected or not rejected. The critical values depend on the chosen significance level and whether the test is one-tailed or two-tailed, determining where the observed test statistic must fall to reject the null hypothesis.
๐Ÿ’กConfidence Level
The confidence level, denoted as C in the video, represents the percentage of all possible samples that can be expected to include the true population parameter. A 95% confidence level implies that if the same population is sampled repeatedly, 95% of the time the true mean would fall within the calculated confidence interval. The video relates the confidence level to the significance level, where C plus alpha equals 1.
๐Ÿ’กRejection Region
The rejection region is the range of values for which the null hypothesis is rejected in favor of the alternative hypothesis. It is determined by the significance level and the critical values. In the video, the rejection regions are shaded areas on either side of the distribution in a two-tailed test, and on one side in a one-tailed test, indicating where the test statistic must fall to reject the null hypothesis.
๐Ÿ’กTest Statistic
The test statistic, such as a Z value in the video, is a standardized value used to compare the observed data with the null hypothesis. It quantifies the distance of the sample statistic from the hypothesized parameter value under the null hypothesis. The decision to reject or not reject the null hypothesis is based on whether this test statistic falls within the rejection region defined by the critical values.
Highlights

Explanation of when to use a one-tailed test or a two-tailed test in hypothesis testing.

Introduction of the concept of null hypothesis with the example of the average mass of potato chip bags.

Definition of alternative hypothesis and its role in determining the type of test.

Clarification that an alternative hypothesis not equaling a specific value indicates a two-tailed test.

Illustration of a normal distribution and the division between rejection and fail-to-reject regions.

Explanation of critical values and their significance in hypothesis testing.

Introduction of the concept of confidence level and its relation to alpha, the significance level.

Breakdown of the significance level into two parts for a two-tailed test.

Explanation of how to decide on rejecting or not rejecting the null hypothesis.

Introduction and differentiation between left-tail and right-tail tests.

Explanation of when to use a left-tail test based on the alternative hypothesis.

Explanation of when to use a right-tail test based on the alternative hypothesis.

Clarification on the relationship between the type of test and the alternative hypothesis statement.

Summary of how the direction of the alternative hypothesis influences the choice of test.

Closing remarks and encouragement to subscribe for more educational content.

Transcripts

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