Question

A quality assurance inspector at a donut factory, checks for product quality using a random sample of 7 donuts from a batch of 38, with 14 cake donuts and 24 glazed donuts. Let p^ be the proportion of cake donuts in the sample.
Is the 10% condition met in this case?

Is the Normal condition met in this case?

Answer 1

Answer:

A: The 10 percent condition states that the population is greater than 10 times the sample, or 10n. In other words, the sample size must be no more than 10 percent of the population. In this problem, the sample size is 7, and the population is 38. This means that 38>10n, or 38>10 times 7, or 70. 38 is not greater than 70, therefor the 10 percent condition is not met in this case. 

B: In this problem, p, or the population proportion is 14/38. The conditions of normality are that n times p and n times 1-p are both greater than 5. n=38 and p, as stated, equals 14/38. This means that n times p equals 14, and n times 1 minus p equals 24, which are both greater than 5. This means that both of the normality condition have been met.

Step-by-step explanation:

Answer 2

Answer:

No/maybe and Yes

Step-by-step explanation:

A) The normal condition states that the population must be greater than or equal to 10n. In this case 10 * 7 (sample size) = 70 which is greater than the batch of 38. You could argue that the factory is likely to produce more than 38 donuts, so it may be possible for Samuel to meet the 10% condition if he is talking about more than one batch.

B) The normal condition is met by np $\geq$ 10 and n(1-p) $\geq$ 10.

We already know that the sample size is 7, so all we need to do is find p. Except we don't. The value of p represents probability, and something can not occur more than 100% of the times that it is possible. For this reason p can only be 0 - 1.0. Even at 100% probability, 7 * 1 < 10, so the normal condition can never be met with only 7 samples.