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The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let [tex]p_A[/tex] = the true proportion of defective chips from plant A and [tex]p_B[/tex] = the true proportion of defective chips from plant B.

Which of the following is a correct statement about the conditions for this test?

A. The random condition is not met.
B. The 10% condition is not met.
C. The Large Counts Condition is not met.
D. All conditions for inference are met.

Answer :

The conditions for performing a hypothesis test on the proportions of defective chips from plant A and plant B are all met. The randomness, 10% condition, and the Large Counts condition (success-failure condition) are satisfied, meaning both the number of expected successes and failures for the samples are at least 5.Correct choice is option D.

In the scenario where the owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than at plant B, a hypothesis test is typically performed to compare the two proportions,
pA and pB.

When comparing two proportions and checking if conditions for a hypothesis test are satisfied, three conditions must be considered: the randomness condition, the 10% condition, and the Large Counts condition.

For the randomness condition, both samples need to be random. For the 10% condition, the sample size must not exceed 10% of the population, to ensure each pick is independent of the others. Finally, the Large Counts condition requires that the samples meet the
success-failure condition where we check if np and nq for both samples are at least 5. Here, np and nq refer to the expected number of successes and failures, respectively.

Given that the quality control specialist takes a random sample and the plant likely produces more than 800 and 900 chips (10 times the sample sizes), the 10% condition is met.

The observed counts at each plant, 12 out of 80 for plant A and 10 out of 90 for plant B, also satisfy the Large Counts condition because the product of the sample size and the sample proportion, as well as its complement, are both greater than 5

(for plant A: 80(12/80) = 12 and 80(68/80) = 68;

for plant B: 90(10/90) = 10 and 90(80/90) = 80).

Considering all these points, the appropriate choice is D. All conditions for inference are met.

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Rewritten by : Barada

Answer:

D. All conditions for inference are met.

Step-by-step explanation:

For the 10% condition :

x / n ; x = number of defective samples ; n = sample size

For Plant A :

x / n = 12 / 80 = 0.15 (> 0.10)

Plant B:

x / n = 10 / 90 = 0.11 (> 0.10)

The sample sizes are large enough ; n > 30

The questions stated that samples were chosen at random.

Hence, all conditions for inference are met.