The Shapiro-Wilk test is used to assess whether data deviate from which distribution?

• A. Normal distribution
• B. Uniform distribution
• C. Exponential distribution
• D. Binomial distribution

Answer: (A)

The Shapiro-Wilk test is used to check if data come from a normal distribution. It tests the null hypothesis that the sample is drawn from a normal distribution with unknown mean and variance. The test computes a W statistic that compares the order statistics of the sample to what a normal distribution would produce; values near 1 and a large p-value indicate the data are consistent with normality, while a small p-value suggests the data depart from normality. This test is particularly powerful for detecting non-normality in small to moderate samples, making it a common choice for assessing whether the assumption of normality holds. It is not designed to assess deviation from other distributions such as Uniform, Exponential, or Binomial.