Question

Fill volumes, in oz, of a large number of beverage cans were measured, with X¯¯¯=11.98 and σX¯¯¯=0.02 . Use this information to find the P-value for testing H0 : μ = 12.03 versus H1 : μ ≠ 12.03. The P-value is _______

Answer 1

The P-value for the test is approximately 0.0124.

Step-by-step explanation:

To find the P-value for testing H0: μ = 12.03 versus H1: μ ≠ 12.03, we need to use the Z-test statistic formula:

Z = (X¯¯¯ - μ) / (σX¯¯¯)

Given X¯¯¯ = 11.98, σX¯¯¯ = 0.02, and μ = 12.03:

Z = (11.98 - 12.03) / 0.02 = -2.50

We need to find the probability of obtaining a Z-value less than -2.50 and the probability of obtaining a Z-value greater than 2.50. Since the alternative hypothesis is two-sided, we double the probability:

P-value = 2 * P(Z > 2.50) = 2 * P(Z < -2.50)

Using a Z-table or calculator, we find that P(Z < -2.50) = 0.0062. Therefore, the P-value for the test is approximately 0.0124.