A teacher has a large container of blue, red, and green beads. She reports to the students that the proportion of blue beads in the container is 0.30. The students feel the proportion of blue beads is lower than 0.30. A student randomly selects 60 beads and finds that 12 of the beads are blue. The P-value for the test of the hypotheses, H0:p=0.30 and Ha:p<0.30, is 0.045. What is the correct interpretation of this value?
Answer
A
There is a 4.5% chance the proportion of blue beads in the container is 0.3.
B
Assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the null hypothesis is true.
C
Assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the sample proportion would be 0.20 or less by chance alone.
D
Assuming the true proportion of blue beads in the container is less than 0.30, there is a 4.5% probability that the sample proportion would be 0.20 or less by chance alone.
Explanation
The sample proportion is 12/60 = 0.20. A P-value is calculated assuming the null hypothesis is true; here, it is the probability of getting a sample proportion of 0.20 or less by chance alone if the true proportion is 0.30. That matches choice C. The P-value is not the probability that the null hypothesis itself is true.
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