Final answer:
d) Median test. The appropriate tool for validating central tendency for non-normally distributed continuous data is the median test.
Step-by-step explanation:
The correct answer is option d) Median test. To validate the central tendency for a continuous project Y when the distribution is not normal, a median test is often used. This test is nonparametric and does not assume normality in the data.
A t-test and ANOVA typically require the assumption of normal distribution in the populations being compared, which does not apply here. A Chi-square test could be used to test for independence or goodness-of-fit but is not usually the primary tool for assessing central tendency when the data is not normally distributed.
The median test focuses on whether two or more medians are different, and it does this by comparing the number of data points above and below a certain value, often the overall median of the data sets combined.
In the various scenarios presented, the Chi-square test can be used for testing a single variance or for assessing homogeneity between two data sets to see if they come from the same distribution.
The T-test can be used when the sample size is small, and the population variance is unknown, specifically when the population is normal.
In contrast, ANOVA is employed to compare the means of three or more populations, assuming normal distribution and equal variances across these populations.