What is the alternative hypothesis (H1) for the goodness-of-fit test concerning normal distribution?

What is the alternative hypothesis (H1) for the goodness-of-fit test concerning normal distribution?

• A. The data does not follow a normal distribution.
• B. The data is normally distributed.
• C. The data follows a binomial distribution.
• D. The data follows a uniform distribution.

Answer: (A)

In the context of a goodness-of-fit test for normal distribution, the alternative hypothesis (H1) represents what we are testing for in opposition to the null hypothesis (H0). The null hypothesis typically states that the data follows a specific distribution—in this case, a normal distribution. Therefore, the alternative hypothesis must assert that the data does not conform to this normal distribution. Choosing that the data does not follow a normal distribution captures the essence of what H1 represents in this context. If the statistical analysis reveals sufficient evidence to reject the null hypothesis, it supports the conclusion that the data deviates from normality. Thus, option A is the correct formulation for the alternative hypothesis in this scenario.

In the context of a goodness-of-fit test for normal distribution, the alternative hypothesis (H1) represents what we are testing for in opposition to the null hypothesis (H0). The null hypothesis typically states that the data follows a specific distribution—in this case, a normal distribution. Therefore, the alternative hypothesis must assert that the data does not conform to this normal distribution.

Choosing that the data does not follow a normal distribution captures the essence of what H1 represents in this context. If the statistical analysis reveals sufficient evidence to reject the null hypothesis, it supports the conclusion that the data deviates from normality. Thus, option A is the correct formulation for the alternative hypothesis in this scenario.