Answer :
To test your suspicion about the mean SSHA score of incoming freshmen, you need to set up a hypothesis test. A hypothesis test involves two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).
Null Hypothesis (H0): This is the statement you want to test against. It usually reflects the current understanding or the status quo. In this case, you suspect that the mean for incoming freshmen is different from the typical average of 115. So the null hypothesis is that the mean \( \mu \) of the incoming freshmen is equal to 115. Formally, you write this as:
\[ H_0: \mu = 115 \]
Alternative Hypothesis (Ha): This hypothesis reflects your suspicion or the effect you want to detect. Since you suspect the mean might be different (either higher or lower), you will use a two-tailed test, which is reflected by the \( \neq \) (not equal) sign. So the alternative hypothesis is:
\[ H_a: \mu \neq 115 \]
Given these hypotheses, you would conduct a hypothesis test to determine whether the sample mean of 116.2 is statistically significantly different from 115.
Therefore, the correct multiple-choice option is:
H0:μ=115 versus Ha:μ≠115.
