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    X. Understanding Hypothesis Testing PDF

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    Brian Garcia
    This document discusses hypothesis testing, which involves hypothesizing about population parameters and subjecting the hypotheses to statistical tests using sample data. It describes the two types of hypotheses - the null hypothesis, which states there is no difference or effect, and the alternative hypothesis. It provides examples of stating hypotheses, determining critical values, and conducting hypothesis tests using the traditional method by specifying the null and alternative hypotheses, checking assumptions, choosing a significance level, selecting a test statistic, stating the decision rule, and making a conclusion.

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    X. Understanding Hypothesis Testing PDF

    Uploaded by

    Brian Garcia
    69 views38 pages
    This document discusses hypothesis testing, which involves hypothesizing about population parameters and subjecting the hypotheses to statistical tests using sample data. It describes the two types of hypotheses - the null hypothesis, which states there is no difference or effect, and the alternative hypothesis. It provides examples of stating hypotheses, determining critical values, and conducting hypothesis tests using the traditional method by specifying the null and alternative hypotheses, checking assumptions, choosing a significance level, selecting a test statistic, stating the decision rule, and making a conclusion.

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    This document discusses hypothesis testing, which involves hypothesizing about population parameters and subjecting the hypotheses to statistical tests using sample data. It describes the two types of hypotheses - the null hypothesis, which states there is no difference or effect, and the alternative hypothesis. It provides examples of stating hypotheses, determining critical values, and conducting hypothesis tests using the traditional method by specifying the null and alternative hypotheses, checking assumptions, choosing a significance level, selecting a test statistic, stating the decision rule, and making a conclusion.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    69 views38 pages

    X. Understanding Hypothesis Testing PDF

    Uploaded by

    Brian Garcia
    This document discusses hypothesis testing, which involves hypothesizing about population parameters and subjecting the hypotheses to statistical tests using sample data. It describes the two types of hypotheses - the null hypothesis, which states there is no difference or effect, and the alternative hypothesis. It provides examples of stating hypotheses, determining critical values, and conducting hypothesis tests using the traditional method by specifying the null and alternative hypotheses, checking assumptions, choosing a significance level, selecting a test statistic, stating the decision rule, and making a conclusion.

    Copyright:

    © All Rights Reserved
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    of 38

    UNDERSTANDING

    HYPOTHESIS TESTING
    HYPOTHESIS TESTING – hypothesizing
    about the population parameter and
    subjecting the hypothesis to a test. It is
    a decision-making process for
    evaluating claims about a population
    based on characteristics of a sample
    purportedly coming from the
    population. The decision is whether
    the characteristic is acceptable or not.
    Two types of Hypotheses:
    1. Null – A statement that there is no
    difference between a parameter and a
    specific value, or that there is no difference
    between two parameters.
    2. Alternative Hypothesis – when the null is
    rejected, alternative hypothesis allows for
    the possibility of many values. A statement
    that there is a difference between a
    parameter and a specific value, or that there
    is a difference between two parameters.
    Null Hypothesis
    States the exact value about
    the parameter, starting point of
    investigation, first statement to
    be made.
    EXAMPLE. Vincent claims that the average
    capacity of a snack that he has is 50g. Is
    the claim true?
    To test the claim, the members of a
    consumer group did the following:
    a. Get a sample of 100 such snacks.
    b. Calculate the capacity of each snack.
    c. Compare the sample mean and claim.
    The observed mean capacity: 43g, sd=5
    Right-tailed Direction
    - Involves words like greater than,
    efficient, improves, effective,
    increases etc.

    Left-tailed Direction
    - Involves words like less than,
    inefficient, decrease, smaller etc.
    EXAMPLE. Raven wants to know if listening to
    popular music affect the performance of the
    students. A class of 100 grade 11 students
    was used in the experiment. The mean score
    was 85 and the standard deviation is 10. A
    previous study revealed that µ = 82 and the
    standard deviation 𝝈 = 10.
    1. State the null and the alternative
    hypotheses in words and in symbols.
    2. State whether the test is directional or
    non-directional.
    EXAMPLE. Arkeen believes that
    using organic fertilizers on her
    plants will yield greater income.
    Her average income from the
    past was P300,000 per year.
    State the hypotheses in symbols.
    A non-directional test is also
    called a two-tailed test.
    A directional test may either be
    left-tailed or right-tailed.
    EXPLORING
    MORE ELEMENTS
    OF HYPOTHESIS TESTING
    Four Possible Outcomes in Decision-Making
    (Type I error - 𝛼, Type II error - 𝛽)
    Decisions about the

    Reject Do not Reject


    (Or accept Null
    H.)
    is Type I error Correct
    Reality true. Decision

    is Correct Type II error


    false. Decision
    UNDERSTANDING ERRORS
    EXAMPLE. Zeth insists that he is 14
    years old when, in fact, he is 17
    years old. What error is Zeth
    committing?
    EXAMPLE. Stephen says that he is
    not bald. His hairline is just
    receding. Is he committing an
    error? If so, what type of error?
    EXAMPLE. Alfross plans to
    hunting the Philippine monkey-
    eating eagle believing that it’s a
    proof of his mettle. What type of
    error is this?
    TYPES OF ERRORS
    ERROR TYPE PROBABILITY CORRECT TYPE PROBABILITY
    IN DECISION
    DECISION

    Reject a I 𝛼 Accept a A 1-𝛼


    true true
    Null H. Null H.

    Accept a II 𝛽 Reject a B 1-𝛽


    False false
    Null H. Null H.
    DETERMINING CRITICAL VALUES
    For each of the given, draw the normal
    curve , locate the z-value and indicate if the
    z-value is in the rejection region or in the
    acceptance region.
    1. z=2, 95% confidence, two-tailed
    2. z=-2.68, 95% confidence, two-tailed
    3. z=1, =-8, 95% confidence, two-tailed
    4. z=1.33, 99% confidence, two-tailed
    5. z=-4.0, 99% confidence, two-tailed
    ANSWER.
    PAGE 225
    EXERCISES ITEMS 4 & 5
    PAGE 232
    EXERCISES ITEMS 3, 4, & 5
    ANSWERS ONLY
    CONDUCTING
    HYPOTHESIS TEST
    USING THE
    TRADITIONAL
    METHOD
    TESTS OF SIGNIFICANCE
    - The practical statistical procedures that
    employ in hypothesis testing.

    SIGNIFICANCE LEVEL OF A TEST


    - The probability of committing a Type I
    error.

    For any hypothesis test,


    p value = probability of committing a Type I error
    •For example, comparing two means.
    • If p≤.05 of asserting that there is a
    difference, when no such difference
    between the two means exists, then
    the difference is said to be significant
    at the 0.05 or 5%, or less level.
    CONDUCTING HYPOTHESIS
    IN TWO WAYS
    1. Traditional or classical method
    2. P-value method

    Test Statistic – a value used to


    determine the probability needed in
    decision-making.
    STEPS IN HYPOTHESIS TESTING
    (Traditional Method)
    Step 1. Describe the population
    parameter of interest. (e.g. Mean,
    proportion)
    Step 2. Formulate the hypothesis: the
    null and alternative hypothesis. State a
    null hypothesis in a such a way that a
    Type I error can be calculated.
    Step 3. Check the assumptions.
    * Is the sample size large enough
    to apply Central Limit Theorem (CLT)?
    * Do small samples come from
    normally distributed populations?
    * Are the samples selected
    randomly?
    STEP 4. Choose a significance level size for
    𝛼. Make a 𝛼 small when the consequences
    of rejecting a true is severe.
    * Is the test two-tailed or one-tailed?
    * Get the critical values from the test
    statistic table.
    * Establish the critical regions.
    Optional: Draw a normal curve, draw
    vertical lines through the critical values,
    and shade the rejection region.
    STEP 5. Select the appropriate test
    statistic.
    * Compute the test statistic using
    the appropriate formula.
    Step 6. State the decision rule for
    rejecting or not rejecting the .
    Step 7. Compare the computed test
    statistic and the critical value. Then,
    based on the decision rule, decide
    whether to reject or not to reject
    (accept) . Interpret the result.
    Optional: Take a course of action.
    LARGE SAMPLE-TEST CONCERNING
    THE MEAN 𝝁 OF A POPULATION

    One Population Test – a test conducted


    on one sample purportedly coming
    from a population with mean 𝝁.
    Sometimes called significance test for a
    single mean.
    Two cases to consider for testing the
    mean of s single proportion:
    1. The sample is large (n ≥ 30). Thus,
    we can apply the CLT and use the
    normal curve as a model.
    2. When CLT is applied, the sample
    standard deviation ‘s’ may be used
    as an estimate of the population
    standard deviation 𝝈 when the value
    of 𝝈 is unknown.
    EXAMPLE. Felicity owns a factory that
    sells a particular bottled shampoo
    claims that the average capacity of
    their product is 250 ml. To test the
    claim, a consumer group gets a sample
    of 100 such bottles, calculate the
    capacity of each bottle, and then find
    the mean capacity to be 248 ml. The
    standard deviation is 5 ml. Is the claim
    true?
    STATING HYPOTHESES
    Table showing Rejection Regions for a
    Common Values of 𝛼
    Alternative Hypothesis
    𝛼 Left-tailed Right-tailed Two-tailed

    𝛼 = .10 z < -1.28 z > 1.28 z < -1.645 or


    z > 1.645
    𝛼 = .05 z < -1.645
    𝛼 = .01 z < -2.33
    ANSWER.
    PAGES 243-245
    EXERCISES
    A, C, E, F
    BOYS – ODD NUMBERS
    GIRLS – EVEN NUMBERS
    ANSWERS ONLY

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