Perform the Indicated Hypothesis Test $$\alpha = 0.05$$ $\text { Day Students}$

question 46

Essay

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
-A statistics teacher wants to see whether there is a significant difference between the variance of the ages of day
students and the variance of the ages of night students. A random sample of 31 students is selected from each
group. The data are given below. Test the claim that there is no difference between the variances of the two
groups.
Use $$\alpha = 0.05$$ $\text { Day Students}$
$\begin{array} { l l l l l l l l l l l } 22 & 24 & 24 & 23 & 19 & 19 & 23 & 22 & 18 & 21 & 21 \\18 & 18 & 25 & 29 & 24 & 23 & 22 & 22 & 21 & 20 & 20 \\20 & 27 & 17 & 19 & 18 & 21 & 20 & 23 & 26 & &\end{array}$ $\text {Evening Students}$
$\begin{array} { l l l l l l l l l l l } 18 & 23 & 25 & 23 & 21 & 21 & 23 & 24 & 27 & 31 & 34 \\20 & 20 & 23 & 19 & 25 & 24 & 27 & 23 & 20 & 20 & 21 \\25 & 24 & 23 & 28 & 20 & 19 & 23 & 24 & 20 & &\end{array}$

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Definitions:

Ethnic Minorities

Groups within a community who have different national or cultural traditions from the main population, often with a history of less power or representation.

Reliability

The degree to which an assessment tool produces stable and consistent results across multiple administrations under similar conditions.

Validity

The quality of being logically or factually sound; the degree to which a concept, conclusion, or measurement is well-founded and corresponds accurately to the real world.

Personality Assessment

The use of standardized tests and tools to evaluate an individual's character, temperament, and personality traits.