The national average SAT score is roughly 1500 . We would like to see if the high school seniors who apply to Duke have higher than average SAT scores. We randomly sample 100 applicants' files and record their SAT scores. Which of the following is the correct set of hypotheses for this research question? Hint: think about how many samples we have data from. OH $$ H_{0}: x=1500 ; H_{A}: x1500 $$ H $$ H_{0}: P=1500 ; H_{A}: P1500 $$ $$ H_{0}: \mu_{ ext {Duke }}=\mu=1500 ; H_{A}: \mu1500 $$ $$ H_{0}: \mu=1500 ; H_{A}: \mu
eq 1500 $$

Question

The national average SAT score is roughly 1500 . We would like to see if the high school seniors who apply to Duke have higher than average SAT scores. We randomly sample 100 applicants' files and record their SAT scores. Which of the following is the correct set of hypotheses for this research question? Hint: think about how many samples we have data from. OH $$ H_{0}: x=1500 ; H_{A}: x>1500 $$ H $$ H_{0}: P=1500 ; H_{A}: P>1500 $$ $$ H_{0}: \mu_{	ext {Duke }}=\mu=1500 ; H_{A}: \mu>1500 $$ $$ H_{0}: \mu=1500 ; H_{A}: \mu 
eq 1500 $$

UpStudy AI · Accepted Answer

To determine the correct set of hypotheses for the research question regarding the SAT scores of high school seniors applying to Duke, we need to consider the following:

1. **Population Parameter**: We are interested in the average SAT score of the applicants to Duke, which is represented by the population mean $$ \mu $$.

2. **Null Hypothesis ($$ H_0 $$)**: This hypothesis states that there is no difference or effect. In this case, it would assert that the average SAT score of Duke applicants is equal to the national average, which is 1500.

3. **Alternative Hypothesis ($$ H_A $$)**: This hypothesis represents what we are trying to find evidence for. Here, we want to see if the average SAT score of Duke applicants is greater than the national average.

Given these points, the correct hypotheses can be formulated as follows:

- **Null Hypothesis**: $$ H_0: \mu = 1500 $$ (The average SAT score of Duke applicants is equal to the national average.)
- **Alternative Hypothesis**: $$ H_A: \mu > 1500 $$ (The average SAT score of Duke applicants is greater than the national average.)

Thus, the correct set of hypotheses for this research question is:

$$
H_{0}: \mu = 1500 ; H_{A}: \mu > 1500
$$

This corresponds to the option:

$$ H_{0}: \mu_{\text {Duke }}=\mu=1500 ; H_{A}: \mu>1500 $$
The correct hypotheses are: - $$ H_{0}: \mu = 1500 $$ - $$ H_{A}: \mu > 1500 $$ This corresponds to option C.

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