Hypothesis testing for normal distributions is a statistical method to determine if a sample mean significantly differs from a population mean. It involves formulating hypotheses, calculating test statistics, and comparing these to critical values to infer about the population. The process is crucial for researchers to make informed decisions based on sample data, using one-tailed or two-tailed tests depending on the direction of the effect they are investigating.
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Hypothesis testing is a statistical procedure used to infer about a population mean based on sample data
Assumptions of Normal Distribution and Known Variance
Hypothesis testing assumes that the sample is drawn from a normally distributed population with known variance
Central Limit Theorem
The central limit theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean will approximate a normal distribution
The probability of observing a sample mean as extreme as, or more extreme than, the one measured is calculated under the assumption that the null hypothesis is true
The initial step in hypothesis testing is to articulate the null hypothesis and the alternative hypothesis
The test statistic, such as the z-score, is calculated to determine the likelihood of the observed sample mean under the null hypothesis
The test statistic is compared to critical values, which are determined based on the significance level and the distribution of the test statistic under the null hypothesis
A one-tailed test is used when the research question predicts a specific direction of the effect
A two-tailed test is appropriate when any significant difference from the hypothesized value is of interest
Critical values are used to determine the rejection and non-rejection regions in a hypothesis test
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A ______ test is applied when the research anticipates the effect to be in a particular direction, such as higher or lower than a specific value.
one-tailed
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Definition of critical values in hypothesis testing
Cutoff points separating rejection and non-rejection regions based on significance level and test statistic distribution under null hypothesis.
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Critical values in one-tailed vs two-tailed tests
One-tailed test uses one critical value for rejection region; two-tailed test uses two, one for each end of the distribution.
