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A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspected. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected?

A. H0:p=0.12Ha:p<0.12 A
B. H0:p=0.12Ha:p>0.12 B
C. H0:p=0.06Ha:p<0.06 C
D. H0:pˆ=0.06Ha:pˆ>0.06 D
E. H0:pˆ=0.12Ha:pˆ<0.12 E

1 Answer

4 votes

Answer: A.


H_0:p=0.12\\\\H_a:p<0.12

Explanation:

Null hypothesis
(H_0) : A statement describing population parameters as per the objective of the study. It usually takes "≤,≥,=" signs.

Alternative hypothesis
(H_a): A statement describing population parameters as per the objective of the study. It usually takes ">, <, ≠" signs.

Let p be the proportion of screens that will be rejected.

12 percent of the screens manufactured using a previous process were rejected at the final inspection.

(i.e. p= 0.12)

Objective of the study = whether the new process reduces the population proportion of screens that will be rejected

i.e. p< 0.12

So, the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected:


H_0:p=0.12\\\\H_a:p<0.12

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