If the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the ...

Ans. #1

TRUE

Ans. #2

TRUE

Ans. #3

The Poisson distribution has a very special characteristic, the standard deviation is equal to the square root of the mean. Thus, when the mean is small, the standard deviation is also small making it easier to plan. However, in hours where the mean arrival rate is higher, the standard deviation is also higher, thereby causing staffing problems.

Ans. #4

The binomial distribution is perfectly symmetric when p = 0.50 for any size sample. It also approaches symmetry when p is not equal to 0.50 as the sample size increases.

Ans. #5

First, using the Poisson distribution, the probability of exactly 1 defect when 1 door panel is inspected is 0.3614. The probability of twice that many defects (x = 2 ) when 2 door panels are examined is 0.2613. The reason that these probabilities are different, even though it might seem like they should be the same, is that when the mean is changed from 1.2 to 2.4 when going from 1 to 2 door panels, the total probability (that sums to 1.0 for the probability distribution) is spread over more possible outcomes, and that means that the probability of any one individual value occurring will be lower.

Ans. #6

The sampling plan calls for a random sample of n =10 items with a cut-off of a = 1 red items. If 1 or fewer reds are found the shipment will be accepted; otherwise it will be rejected. The objectives are:
1. If the shipment meets the contract (no greater than 10 percent reds) we want to accept the shipment.
2. If the shipment violates the contract (more than 10 percent reds) we want to reject the shipment.

The binomial distribution can be used to determine the probability of meeting these objectives. First, we find P(x  = 1, n = 10, p = 0.10 ) from the binomial table to be 0.7361. This is the probability that we will meet the first objective. Next, we find P(x  2, n = 10, p = 0.20 ) from the binomial table to be 0.6242, which is the probability of meeting the second objective. We would like both probabilities to be high (close to 1.000 ). These are middle-of-the-road and we most likely would conclude that the plan as stated is inadequate. However, the final decision needs to be based on the costs of not meeting the desired objectives.

Ans. #7

When p > 0.50, you have two options. The first option is to think in terms of failures rather than successesfor instance, if the sample size is n =10 and we originally want to find the probability of 3 successes when p = 0.70. Instead we can switch the problem around and instead of finding the probability of 3 successes, we can find the probability of 7 failures with the probability of a failure being p = 0.30. An alternative method is to use the q values at the bottom of each column (if the binomial distribution table being used has these values). Treat these as if they were the p values. Then locate the number of successes of interest in the right-hand column of the binomial table. Both methods will give the same result.

Just confirmed the same answer from my friend, thanks