a-technician-monitors-the-daily-performance-of-a-machine-and-records-whether-it-

Question

A technician monitors the daily performance of a machine and records whether it passes or fails quality checks over $20$ consecutive days. The outcomes are shown as a sequence of $P$ (pass) and $F$ (fail):

$P P F F F P F P P F F F P F P P P F F P$

The technician claims that the pattern is not random. State the appropriate null and alternative hypotheses.

Accepted Answer

$H sub 0 colon$ The sequence is random

$H_{a} :$ The sequence is not random

Answer

$H sub 0 colon$ The number of runs is too small

$H_{a} :$ The number of runs is large

Answer

$H sub 0 colon$ The machine failed frequently

$H_{a} :$ The machine failed randomly

Answer

$H sub 0 colon$ There are too many passes

$H_{a} :$ There are not enough fails