Consider the Hypotheses H₀: σ² = 169, H_A: σ² ≠

question 55

Essay

Consider the hypotheses H₀: σ² = 169, H_A: σ² ≠ 169. A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the p-value approach.

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Definitions:

Rejection Region

The range of values in hypothesis testing for which the null hypothesis is rejected, based on the chosen level of significance.

Two-Sided Hypothesis

A hypothesis test that allows for an effect in two directions, either greater than or less than a specific value, not limiting the expected effect to one direction.

Null Hypothesis

A stated hypothesis that there is no significant difference or effect, often denoted as H0, to be tested against the alternative hypothesis.

Type I Error

The incorrect rejection of a true null hypothesis or a false positive in hypothesis testing.