Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: σ^2 = 142
H0: σ ≠ 142

검증된 단계별 안내

Step 1: Understand the null hypothesis (H0) and the alternative hypothesis (Ha). In this case, H0 states that the population variance (σ^2) is equal to 142, while Ha states that the population variance is not equal to 142.

Step 2: Recognize the type of comparison being made in the alternative hypothesis (Ha). If Ha uses '≠', it indicates that the test is looking for any difference, either greater than or less than the value specified in H0.

Step 3: Recall that a hypothesis test with '≠' in the alternative hypothesis is a two-tailed test because it considers deviations in both directions (greater than and less than the specified value).

Step 4: Confirm that the test is two-tailed by noting that the rejection regions for the null hypothesis will be in both tails of the distribution.

Step 5: Conclude that this hypothesis test is a two-tailed test based on the structure of the alternative hypothesis (Ha: σ^2 ≠ 142).

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주요 개념

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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (Ha), which indicates the presence of an effect or difference. The goal is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative.

Types of Hypothesis Tests

Hypothesis tests can be classified as left-tailed, right-tailed, or two-tailed based on the direction of the alternative hypothesis. A left-tailed test is used when Ha suggests that a parameter is less than a certain value, while a right-tailed test is used when Ha suggests it is greater. A two-tailed test is appropriate when Ha indicates that the parameter is simply different from a specified value, without specifying a direction.

Variance and Standard Deviation

Variance (σ^2) is a measure of the dispersion of a set of data points around their mean, indicating how much the values differ from the average. In hypothesis testing, the population variance is often tested to understand the variability of the data. The null hypothesis in this case (H0: σ ≠ 142) suggests that the population variance is not equal to 142, while the alternative hypothesis (Ha: σ^2 = 142) posits that it is equal to this value.

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.Ha: σ^2 = 142H0: σ ≠ 142