A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a random sample of 100 chips from the day’s production and determines that there were 12 defective chips. He wants to construct a 90% confidence interval for the true proportion of defective chips from the day’s production. Are the conditions for inference met?

A. Yes, the conditions for inference are met.
B. No, the 10% condition is not met.
C. No, the randomness condition is not met.
D. No, the Large Counts Condition is not met.

The conditions for inference are met. The sample size is sufficiently large (n = 100) for the normal approximation to the sampling distribution of the sample proportion to be valid.

The 10% condition is also met, as the sample size (100) is less than 10% of the total population of computer chips produced in a day.

Therefore, the quality control specialist can proceed with constructing a 90% confidence interval for the true proportion of defective chips from the day’s production

Qwcold Qwcold · Answer 2 · 2024-07-19T03:40:50-04:00

Final answer:

First option is correct. Assuming the sample of chips is random and less than 10% of the day's production, the Large Counts condition is met. Therefore, the conditions for inference are likely met, and the quality control specialist can construct a 90% confidence interval for the true proportion of defective chips.

Explanation:

When constructing a confidence interval for the true proportion of defective chips from a day's production, there are certain conditions for inference that must be met. The conditions typically include randomness, independence, and the Large Counts condition. The randomness condition is presumed to be met if the sample is said to be randomly selected. The independence condition often includes the 10% condition, which states that the sample size should be no more than 10% of the population to avoid needing a finite population correction factor. In this case, the 10% condition is likely met unless the batch of chips produced that day was fewer than 1000. The Large Counts condition is met if both np and n(1-p) are greater than 10, where n is the sample size and p is the sample proportion. Here, with 100 sampled chips and 12 defected, np=12 and n(1-p)=88, both of which are greater than 10, indicating that this condition is met as well.

Therefore, assuming the sample is indeed random and representative of the day's production, and that the day's production is more than 1000 chips (so the 10% condition holds), the conditions for inference are met. Thus, the quality control specialist can proceed to construct the 90% confidence interval for the true proportion of defective chips.