Ramsay Test Sample 6

Question 1

A quality technician uses a stratified random sampling plan on a production run of 2,400 parts divided equally among 4 shifts. If 60 total samples are required, how many parts should be sampled per shift to maintain proportional representation?

Accepted Answer

15

Answer

Stratified random sampling requires proportional allocation across strata (shifts). With 4 equal shifts and 60 total samples, each shift contributes 60 ÷ 4 = 15 samples. This ensures each stratum is represented in proportion to its size in the population.

Question 2

When using a systematic sampling method on a conveyor line producing 900 units per hour, a technician must collect 30 samples per hour. What is the correct sampling interval, and from which unit should the first sample be randomly selected?

Accepted Answer

Every 30th unit; first unit selected randomly between 1 and 30

Answer

Systematic sampling interval = population size ÷ sample size = 900 ÷ 30 = 30. The first unit must be chosen randomly within the first interval (1 to 30) to avoid introducing bias; every subsequent unit is selected at the fixed 30-unit interval from there.

Question 3

A process engineer examines a control chart and notices 7 consecutive sample means falling on the same side of the centerline, even though all points remain within the control limits. What is the MOST appropriate conclusion?

Accepted Answer

The pattern indicates a non-random special cause requiring investigation

Answer

The 'run rule' states that 7 or more consecutive points on one side of the centerline signal a non-random, special-cause variation — even if all points are within control limits. The probability of this occurring by chance is less than 1%, indicating a systematic shift in the process mean that must be investigated.

Question 4

A sampling plan specifies an Acceptable Quality Level (AQL) of 1.0% and a Lot Tolerance Percent Defective (LTPD) of 6.0%. If a batch is submitted with a true defect rate of exactly 1.0%, which risk is MOST directly relevant to the producer?

Accepted Answer

Producer's risk (Alpha risk) — probability the lot is rejected despite meeting AQL

Answer

When the true defect rate equals the AQL, the producer's risk (alpha risk, or Type I error) is the concern — the probability that a good lot will be incorrectly rejected by the sampling plan. Consumer's risk (beta risk) applies when a bad lot is incorrectly accepted, which is relevant at the LTPD level.

Question 5

A dimensional inspection uses a sample of n = 25 parts and calculates a sample mean of 50.4 mm and a sample standard deviation of 0.8 mm. What is the standard error of the mean for this sample?

Accepted Answer

0.16 mm

Answer

Standard error of the mean (SEM) = s ÷ √n = 0.8 ÷ √25 = 0.8 ÷ 5 = 0.16 mm. The SEM measures how much the sample mean is expected to vary from the true population mean — it decreases as sample size increases, which is why larger samples yield more reliable estimates.

Ramsay Test Practice Test

Ramsay Test Practice Test

Ramsay Test Sample 6