Math  /  Data & Statistics

QuestionOver 8-2 \& 8-3) Question 3 or 12 This questioni:
Suppose a principal claims that the mean test score at her school is greater than the national average. She performs a hypothesis test and finds the test statistic to be t=1.77t=1.77 and she knows the critical value for this test to be t=1.98t=1.98. What can she conclude? A. There is not sufficient evidence to support her claim since the test statistic does not fall in the critical region. B. There is not sufficient evidence to support her claim since the test statistic falls in the critical region. C. There is sufficient evidence to support her claim since the test statistic falls in the critical region. D. There is sufficient evidence to support her claim since the test statistic does not fall in the critical region.

Studdy Solution

STEP 1

What is this asking? Does the principal's test score beat the national average, given her test result and the critical value? Watch out! Don't mix up the test statistic and the critical value!
Also, remember what "critical region" means.

STEP 2

1. Critical Region
2. Conclusion

STEP 3

Alright, let's dive into this hypothesis test!
The principal believes her school's mean test score is *higher* than the national average.
This means she's looking for evidence in the *upper tail* of the distribution.
The **critical region** is the area where, if our test statistic lands there, we reject the *null hypothesis* (that the school's score *isn't* higher).

STEP 4

The **critical value** here is t=1.98t = 1.98.
This sets the boundary for our **critical region**.
Any test statistic *greater* than 1.981.98 falls into the critical region.
Think of it like a hurdle race: 1.981.98 is the hurdle, and the test statistic needs to clear it to be in the critical region!

STEP 5

Now, the principal's **test statistic** is t=1.77t = 1.77.
Is 1.771.77 greater than 1.981.98?
Nope! So, the test statistic *doesn't* fall into the critical region.
It didn't clear the hurdle!

STEP 6

Since the test statistic (t=1.77t = 1.77) is *less than* the critical value (t=1.98t = 1.98), it's *outside* the critical region.
This means there *isn't enough evidence* to reject the null hypothesis.

STEP 7

In simpler terms, the principal's test score isn't high enough to confidently say it's better than the national average.
Bummer! So, the correct answer is A.

STEP 8

The correct answer is A: There is not sufficient evidence to support her claim since the test statistic does not fall in the critical region.

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