1. Evaluating Manufacturing Quality
Quality Assurance EngineerBackground
A factory produces cables with a known historical standard deviation of 15mm. A recent batch of 64 cables yielded an average length of 105mm.
Problem
Determine if the new batch's mean length significantly differs from the target length of 100mm.
How to use
Select 'Mean' as the test type. Enter 105 for Sample Mean, 100 for Hypothesized Mean, 15 for Population Standard Deviation, and 64 for Sample Size.
{
"testType": "mean",
"sampleMean": 105,
"hypothesizedMean": 100,
"populationStandardDeviation": 15,
"sampleSize": 64,
"alternative": "two-sided",
"alpha": 0.05
}Outcome
The calculator outputs a Z-statistic of 2.6667 and a P-value of 0.0077. Since the P-value is less than 0.05, 'rejectNull' is true, indicating the batch is significantly different from the target.