You roll two number cubes. Let event A = You roll an even number on the first cube.
Let event B = You roll a 2 on the second cube.
Are the events independent or dependent? Why?
A. Independent, because they have no outcomes in common.
B. Dependent, because both cubes have six sides.
C. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
O D. Dependent, because 2 is an even number.

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).