Eva Would Like to Determine Whether Her Running Pace Is

question 44

Multiple Choice

Eva would like to determine whether her running pace is more consistent in the afternoon than in the morning.A sample of 10 morning runs (from population 1) has an average pace of 7 minutes, 32 seconds per mile, with a standard deviation of 45 seconds per mile.A sample of 12 afternoon runs (from population 2) has an average pace of 7 minutes, 20 seconds per mile, with a standard deviation of 32 seconds per mile.She assumes that her running times follow a normal distribution in both populations. She uses the data to test the following hypotheses:
H₀: σ₁² ≤ σ₂² (the morning variance is less than or equal to the afternoon variance)
H_A: σ₁² > σ₂² (the morning variance is greater than the afternoon variance)
At a 5% significance level, what is the conclusion of the hypothesis test?

• A)Since the test statistic is greater than the critical value of 2.896, reject the null hypothesis.The evidence supports the claim that the morning variance exceeds the afternoon variance.
• B)Since the test statistic is not greater than the critical value of 2.896, do not reject the null hypothesis.The evidence does not support the claim that the morning variance exceeds the afternoon variance.
• C)Since the test statistic is greater than the critical value of 2.896, reject the null hypothesis.The evidence does not support the claim that the morning variance exceeds the afternoon variance.
• D)Since the test statistic is greater than the critical value of 2.896, do not reject the null hypothesis.The evidence supports the claim that the morning variance exceeds the afternoon variance.

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Definitions:

Good Thinking

The practice of reasoning and decision-making that is logical, informed, and reflective, often leading to effective solutions.

Critical Thinking

The objective analysis and evaluation of an issue in order to form a judgment; involves asking questions, analyzing arguments, and identifying biases.

Cynical

Having a belief that people are motivated purely by self-interest; skeptically distrustful of human sincerity or integrity.

Judgmental

Having or displaying an excessively critical point of view or being quick to make judgments about others.