A clinical psychologist notices that admission to the psychiatric hospital she works at seem to

vary by season. Using a chi-square test, she rejects the null hypothesis that hospital admission
is independent of season. What conclusions can she make?
a. Hospital admissions are greater in the spring.
b. Hospital admissions are greater in the fall than in the winter.
c. There is a relationship between hospital admission and the season.
d. There is no relationship between hospital admission and the season.
I think the answer is c but the chi-square test has me confused.

Without more data, I would also pick C.

Yes, you are correct. The answer is c - There is a relationship between hospital admission and the season.

Let me explain why. The clinical psychologist used a chi-square test to analyze the association between hospital admission and seasons. The chi-square test is a statistical test used to determine if there is a relationship between two categorical variables. In this case, the variables are hospital admission (categorized as either admitted or not admitted) and season (categorized as spring, summer, fall, or winter).

When the psychologist rejected the null hypothesis, she found evidence to suggest that hospital admission is not independent of season. In other words, there is a statistical relationship between hospital admission and the season. However, it is important to note that the chi-square test does not provide information about the direction or magnitude of this relationship. Therefore, it cannot determine which specific seasons have higher admission rates compared to others.

To clarify, while the chi-square test tells us that there is a relationship between hospital admission and the season, further analysis or additional tests would be needed to determine the specific seasons with higher admission rates.

You are correct, the answer is c. When the clinical psychologist rejects the null hypothesis that hospital admission is independent of season using a chi-square test, it means that there is a relationship between hospital admission and the season. In other words, the season is a factor that affects the number of hospital admissions.