A hypothesis test is to be performed. State the null and alternative hypotheses.
-At one school, the average amount of time that tenth-graders spend watching television each week is $21.6$ hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.

Question

A hypothesis test is to be performed. State the null and alternative hypotheses.
-At one school, the average amount of time that tenth-graders spend watching television each week is $21.6$ hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
A) Null hypothesis: mean time $= 21.6$ hours
Alternative hypothesis: mean time $\leq 21.6$ hours
B) Null hypothesis: mean time $> 21.6$ hours
Alternative hypothesis: mean time $< 21$.6 hours
C) Null hypothesis: mean time $= 21.6$ hours
Alternative hypothesis: mean time $< 21.6$ hours
D) Null hypothesis: mean time $< 21$. 6 hours
Alternative hypothesis: mean time $= 21.6$ hours

Quizplus · Accepted Answer

The null hypothesis typically states that there is no effect or no difference, so it would assert that the mean time spent watching television is equal to 21.6 hours. The alternative hypothesis is what the principal hopes to prove, which is that the mean time has decreased, hence it is less than 21.6 hours.

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A Hypothesis Test Is to Be Performed $21.6$ Hours the Principal Introduces a Campaign to Encourage the Students