Statistics: Hypothesis Testing Overview
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Questions and Answers

What is the sample standard deviation of the customer expenditure?

  • R0.75 (correct)
  • R0.50
  • R1.00
  • R1.25
  • The null hypothesis states that there is a significant difference between the parameter values.

    False

    At a 99% confidence level, what is the Z-score used in hypothesis testing?

    2.58

    The _____ hypothesis is not true if there is sufficient evidence against it.

    <p>alternative</p> Signup and view all the answers

    Match the following components with their definitions:

    <p>Z-score = A measure of standard deviations from the mean Confidence Level = Probability that the true parameter lies within the interval Null Hypothesis = Hypothesis that proposes no difference or effect Alternative Hypothesis = Hypothesis that proposes a difference or effect exists</p> Signup and view all the answers

    What would be the conclusion if the test statistic is Z = -2.5 at 1% level of significance?

    <p>Accept the null hypothesis</p> Signup and view all the answers

    A two-tailed test checks for differences in both directions (greater and lesser).

    <p>True</p> Signup and view all the answers

    What is the null hypothesis in the case of Mr.Cake's average daily bread sales?

    <p>Ho: μ = 1500</p> Signup and view all the answers

    In a one-tailed hypothesis test with a significance level of 0.05, what is the critical Z value for rejection in the left tail?

    <p>-1.645</p> Signup and view all the answers

    The null hypothesis is rejected if the test statistic is greater than the critical value in a one-tailed test.

    <p>False</p> Signup and view all the answers

    What is the significance level used in the hypothesis testing example given above?

    <p>0.05</p> Signup and view all the answers

    If a textile company's claim is that the average strength of their fabric is at least 22.7 kg, then the null hypothesis is Ho: μ __________ 22.7 kg.

    <p>≥</p> Signup and view all the answers

    Match the following values with their corresponding confidence levels:

    <p>1.65 = 90% confidence level 1.96 = 95% confidence level 2.58 = 99% confidence level 0.05 = Significance level for 95% confidence</p> Signup and view all the answers

    What conclusion is made if the test statistic calculated is -2.48 when testing the fabric strength claim?

    <p>There is sufficient evidence to conclude the average strength is less than 22.7 kg.</p> Signup and view all the answers

    In hypothesis testing, the alternative hypothesis is denoted as Ha: μ ≤ 22.7 kg when testing against the company's claim.

    <p>False</p> Signup and view all the answers

    What is the test statistic for the example provided in the content?

    <p>-2.48</p> Signup and view all the answers

    What Z-value corresponds to a 95% confidence level?

    <p>1.96</p> Signup and view all the answers

    The Z-table provides probabilities for Z-values greater than or equal to zero only.

    <p>True</p> Signup and view all the answers

    What is the Z-value for a 99% confidence level?

    <p>2.58</p> Signup and view all the answers

    For estimating a finite population when σ is known, we use the ______ method.

    <p>normal</p> Signup and view all the answers

    Match the following confidence levels with their corresponding Z-values:

    <p>90% = 1.65 95% = 1.96 99% = 2.58</p> Signup and view all the answers

    If the population standard deviation (σ) is unknown and the sample size is greater than 30, which method is used for estimation?

    <p>T-method</p> Signup and view all the answers

    In an infinite population, if σ is known, we still estimate using the T-distribution.

    <p>False</p> Signup and view all the answers

    Which Z-value indicates an area to the left of 0.5 in the standard normal distribution?

    <p>0</p> Signup and view all the answers

    The smart packaging company is trying to estimate the average ______ per customer.

    <p>spending</p> Signup and view all the answers

    What value from the Z-table corresponds to a Z-score of 1.0?

    <p>0.3413</p> Signup and view all the answers

    Study Notes

    One-Tailed Hypothesis Tests

    • A one-tailed test focuses on one direction of the alternative hypothesis.
    • The critical region is located in one tail of the distribution.
    • Significance level (α) is the probability of rejecting the null hypothesis when it is true. In one-tailed tests, the significance level is applied entirely to one tail of the distribution.
    • The decision rule depends on whether the test is left-tailed or right-tailed.

    Two-Tailed Hypothesis Tests

    • A two-tailed test considers deviations from the null hypothesis in both directions.
    • The critical region is split between the two tails of the distribution.
    • Significance level (α) is divided between the two tails.
    • The decision rule involves comparing the test statistic to both upper and lower critical values.

    Hypothesis Testing

    • A procedure for evaluating a claim about a population parameter.
    • Hypotheses are statements about the population parameter.
    • The objective is to decide if the evidence supports the claim.
    • Null hypothesis (H₀) is the statement of no effect or no difference.
    • Alternative hypothesis (Hₐ) is the claim being tested.

    Confidence Intervals

    • An interval estimate of a population parameter calculated from a sample statistic.
    • Confidence level represents the probability that the interval contains the true population parameter.
    • Confidence level is expressed as a percentage, e.g., 90%, 95%, 99%.
    • Common confidence levels have corresponding critical values. These critical values define the range within which the population parameter value is likely to fall. The critical values depend on the confidence level to be achieved.

    Sample Size Determination

    • Determining the appropriate sample size needed for a given level of accuracy.
    • Factors such as confidence level, desired margin of error, and population standard deviation or sample standard deviation play a critical role in this process. The sample size required is influenced by both the desired precision of the calculation and the confidence level.

    Standard Error

    • Standard deviation of a sampling distribution of a sample statistic
    • A function of the standard deviation of the population and the sample size; smaller sample sizes tend to give greater variability, leading to a higher standard error

    Examples of Hypothesis Testing

    • Testing average fabric strength
    • Average spending per customer
    • Average number of breads sold daily
    • Number of daily newspaper readers.

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    Related Documents

    One-tailed Test PDF

    Description

    This quiz covers the fundamentals of hypothesis testing, including one-tailed and two-tailed tests. Learn how significance levels and decision rules are applied in different testing scenarios. Test your understanding of key concepts related to evaluating claims about population parameters.

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