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 point 3 0 The students feel the proportion of blue beads is lower than 0 point 3 0 A student randomly selects 60 beads and finds that 12 of the beads are blue. The cap p -value for the test of the hypotheses, ratio of cap h sub 0 to p is equal to 0 point 3 0 and ratio of cap h sub A to p is less than 0 point 3 0 , is 0 point 0 4 5 What is the correct interpretation of this value?
Answer
A
There is a 4 point 5 percent chance the proportion of blue beads in the container is 0 point 3 .
B
Assuming the true proportion of blue beads in the container is less than 0 point 3 0 , there is a 4 point 5 percent probability that the sample proportion would be 0 point 2 0 or less by chance alone.
C
Assuming the true proportion of blue beads in the container is 0 point 3 0 , there is a 4 point 5 percent probability that the sample proportion would be 0 point 2 0 or less by chance alone.
D
Assuming the true proportion of blue beads in the container is 0 point 3 0 , there is a 4 point 5 percent probability that the null hypothesis is true.
Explanation
A p-value is calculated under the assumption that the null hypothesis is true, here that the blue-bead proportion is 0.30. It measures the chance of getting a result at least as extreme in the direction of the alternative; for this lower-tail test, that means a sample proportion of 0.20 or less. Thus, the p-value of 0.045 means a 4.5% probability of such a sample result by chance alone, assuming the true proportion is 0.30. It does not give the probability that the null hypothesis itself is true.
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