CompTIA Data+ (DA0-002)Data AnalysisMedium
A quality control manager is monitoring the weight of cereal boxes coming off an assembly line. The target weight is 450 grams. A sample of 30 boxes is collected, and their average weight is 448 grams with a standard deviation of 5 grams. The manager wants to determine if the average weight of cereal boxes is significantly different from the target weight. Assuming the population standard deviation is unknown, which statistical test should be used?
- AZ-test
- BANOVA
- CTwo-sample t-test
- DOne-sample t-test
Show answer & explanationAnswer & explanation
Correct answer: D. One-sample t-test
The one-sample t-test is appropriate when comparing the mean of a single sample to a known or hypothesized population mean (the target weight in this case), especially when the population standard deviation is unknown and the sample size is relatively small (though n=30 often allows for Z, t-test is safer with unknown population std dev).
Why the other options are wrong
- A. A Z-test would be used if the population standard deviation were known, which it is not in this scenario.
- B. ANOVA is used to compare the means of three or more groups, not a single sample against a target.
- C. A two-sample t-test is used to compare the means of two independent samples, not a single sample against a target.
One-Sample t-test
A parametric hypothesis test used to determine if the mean of a single sample is statistically different from a known or hypothesized population mean, particularly when the population standard deviation is unknown.
- Compares a sample mean to a population mean.
- Assumes the data is approximately normally distributed (especially for small samples).
- Used when population standard deviation is unknown.
Memory trick: One mean, one target, unknown sigma? T-test is your helper!