Question

1. College students listened to either Mozart or silence, and then took an IQ test. Researchers hypothesize that, on average, students perform better on the IQ test after listening to Mozart than after listening to silence.

1. Define the parameter of interest both in words and using the appropriate statistical symbol.
2. State the null and alternative hypotheses.
3. If the p-value of the test is 0.678, can we conclude that there is no difference in IQ scores after listening to Mozart and after listening to silence, on average, in the population of college students? Explain.

Answer 1

a) Suppose the average IQ score of students in IQ score after listening to Mozart be denoted by x̄m and the average IQ score of students in IQ score after listening to silence be denoted by x̄s.

Thus, Our interest in the parameter is the average score of the student in the IQ test. In symbolic form, our interest in the parameter is the x̄m and  x̄s.

b) Null hypothesis H0: On average, in the population of college students, there is no difference in IQ scores after listening to Mozart and after listening to silence. i.e. μm=μs

Alternative hypothesis H1: On average, in the population of college students, there is a difference in IQ scores after listening to Mozart and after listening to silence. i.e. μm ≠ μs.

c) P-value obtained in the test is 0.678 which is greater than 0.05. This implies that we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant and we can conclude that on average, in the population of college students, there is the difference in IQ scores after listening to Mozart and after listening to the silence.