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Provide an appropriate response.

Given [tex]$H_0: p \geq 80\%$[/tex] and [tex]$H_2: p \ \textless \ 80\%$[/tex], determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Select one:
A. two-tailed
B. left-tailed
C. right-tailed

Sagot :

GinnyAnswer
To determine the type of hypothesis test, let's begin by understanding the given hypotheses:

- The null hypothesis [tex]\(H_0\)[/tex]: [tex]\( p \geq 80\% \)[/tex]
- The alternative hypothesis [tex]\(H_2\)[/tex]: [tex]\( p < 80\% \)[/tex]

The null hypothesis [tex]\(H_0\)[/tex] posits that the population proportion [tex]\(p\)[/tex] is at least 80%. Conversely, the alternative hypothesis [tex]\(H_2\)[/tex] claims that the population proportion [tex]\(p\)[/tex] is less than 80%.

Next, consider the direction of the inequality in the alternative hypothesis:

- Since the alternative hypothesis [tex]\(H_2\)[/tex]: [tex]\( p < 80\% \)[/tex] is concerned with whether the proportion [tex]\(p\)[/tex] is less than 80%, it indicates that we are specifically looking for evidence that the population proportion is lower than the stated value.

Therefore, the type of test depends on the direction specified in the alternative hypothesis:
- If the alternative hypothesis tests whether [tex]\(p\)[/tex] is less than a certain value, it is a left-tailed test.
- If it tests whether [tex]\(p\)[/tex] is greater than a certain value, it is a right-tailed test.
- If it tests whether [tex]\(p\)[/tex] is significantly different (either greater or less), it is a two-tailed test.

Given that the alternative hypothesis [tex]\(H_2\)[/tex] states [tex]\( p < 80\% \)[/tex], we are interested in finding evidence that [tex]\(p\)[/tex] is less than 80%, which makes this a left-tailed test.

Thus, the correct answer is:

B. left-tailed
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