Researchers intend to test whether evaluations of learning sources given by students match the theoretical distribution. A categorical variable, X, is measured in the FIVE-point scale. The observed frequencies obtained after having n = 1000 responses processed are shown in the table below along with hypothetical probabilities.

	Excellent	Very Good	Good	Fair	Poor	Total
Observed	132	140	121	63	44	500
Proportions	0.30	0.25	0.20	0.15	0.10	1
Expected

At the significance level, = 0.05, do you have sufficient evidence that the TRUE DISTRIBUTION of students' preferences DIFFERS from what was stated by the null hypothesis?

• Find EXPECTED COUNTS and place them in the table above.
• Evaluate the goodness-of-fit test statistic
• Determine CRITICAL VALUE (or VALUES) required for this procedure
• State Rejection Rule and then formulate your DECISION