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:

Participants' Confidence

The level of belief individuals participating in an experiment or study have in their responses or judgments.

Deductive Reasoning

A logical process where a conclusion is based on the concordance of multiple premises that are generally assumed to be true.

Underconfidence

A cognitive bias in which individuals underestimate their knowledge, abilities, or performance.

Frontal Lobe

A division of the cerebral cortex located just beneath the forehead that contains the motor cortex, premotor cortex, and prefrontal cortex.