Final answer:
The Chi-squared distribution is used for testing a claim about a population standard deviation. The t-distribution is utilized for a population mean when the standard deviation is unknown and sample size is small, while a normal distribution is used for population proportions with large samples. The correct answer is option b) Chi-squared distribution
Step-by-step explanation:
The appropriate sampling distribution for testing a claim about a population standard deviation is the Chi-squared distribution. This choice is based on the properties of the Chi-squared distribution, which is specifically used when dealing with variance and standard deviation in a population.
When the population standard deviations are known, and the sample size is sufficiently large, the z-test, which uses the normal distribution, may be used for testing the population mean. However, for variance or standard deviation, even with known parameters, we rely on the Chi-squared test.
The t-distribution is generally used for hypothesis testing of a population mean when the population standard deviation is unknown and the sample size is not significantly large. For testing population proportions, the normal distribution is used when the sample size is large.