In Testing the Hypotheses $H _ { 0 } : \mu = 60$

question 91

Essay

In testing the hypotheses $H _ { 0 } : \mu = 60$ . $H _ { 1 } : \mu < 60$ .
the following information was given: $\sigma = 5 , \quad n = 100 , \quad \bar { x } = 59 , \quad \alpha = 0.05$ .
a. Calculate the value of the test statistic.
b. Set up the rejection region.
c. Determine the p-value.
d. Interpret the result.

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Definitions:

Ego-oriented Goal

Objectives where the primary focus is on self-improvement relative to one's own past performances, emphasizing personal achievement and mastery.

Competitive

Having a strong desire to compete or succeed, often resulting in direct rivalry.

Controversial

Something that gives rise to public disagreement or debate, reflecting diverse opinions on a subject.

Aggressive

Behavior characterized by assertiveness, dominance, or hostility towards others, potentially resulting in physical or verbal confrontation.