Question

When a truckload of apples arrives at a packing plant, a random sample of 175 apples are selected and examined for bruises and other defects. In reality, 10% of the apples on a particular truck are bruised or otherwise unsatisfactory.
(a) How many standard errors away from 0.1 would you need to go to contain 89% of the sample proportions of bad apples you might expect to find? (3 decimal places)
(b) Suppose you were going to construct an 89% confidence interval from this population. What critical value should you use? (3 decimal places)

Answer 1

The critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

The confidence interval for a population with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose

mean = 10

as, we have 89% confidence interval (5, 15)

where EBM = 5.

To get 89% confidence interval,

mean = 10 of the normal distribution.

Then, the critical value we use is

(10 – 2.5, 10 + 2.5).

So, the critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

Hence, the critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

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