Asked by Abigail Orozco on Jul 15, 2024
Verified
Ten samples of a process measuring the number of returns per 100 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, 11. Find the standard deviation of the sampling distribution. (Hint- Use p-bar formula)
A) There is not enough information.
B) .081
C) 8.1
D) .0273
E) .0863
Standard Deviation
A statistical measure of the dispersion or variation in a set of values, indicating how much the values differ from the average.
Sampling Distribution
The probability distribution of a given statistic based on a random sample, often used to make inferences about the population.
P-bar Formula
A statistical technique used in quality control to determine the proportion of defective items in a batch or process.
- Implement core statistical formulas to figure out control limits and comprehend their contribution to the efficacy of SPC charts.
Verified Answer
RK
Rasel KabirJul 16, 2024
Final Answer :
D
Explanation :
The formula to calculate the standard deviation of the sampling distribution using p-bar is:
SD = sqrt [p-bar(1-p-bar)/n], where p-bar is the sample proportion and n is the sample size.
To find p-bar (sample proportion), we need to add up the number of returns in all the samples and divide by the total number of receipts in all the samples:
p-bar = (10+9+11+7+3+12+8+4+6+11) / (10*100) = 0.0805
Now, we can plug in the values in the formula:
SD = sqrt [0.0805*(1-0.0805)/10*100] = 0.0273
Therefore, the standard deviation of the sampling distribution is 0.0273, which is answer choice D.
SD = sqrt [p-bar(1-p-bar)/n], where p-bar is the sample proportion and n is the sample size.
To find p-bar (sample proportion), we need to add up the number of returns in all the samples and divide by the total number of receipts in all the samples:
p-bar = (10+9+11+7+3+12+8+4+6+11) / (10*100) = 0.0805
Now, we can plug in the values in the formula:
SD = sqrt [0.0805*(1-0.0805)/10*100] = 0.0273
Therefore, the standard deviation of the sampling distribution is 0.0273, which is answer choice D.
Learning Objectives
- Implement core statistical formulas to figure out control limits and comprehend their contribution to the efficacy of SPC charts.