Criteria for Choosing T vs Z Tests
A researcher is investigating whether the mean weight of a batch of produced items is different from 50 grams. Under what conditions should the researcher use a Z-test instead of a T-test to perform a hypothesis test? Describe the key criteria related to sample size, knowledge of population standard deviation, and assumptions about the data […]
Assessing Normality from a Small Dataset
A production manager collects the weights (in grams) of 10 widgets produced in one batch, which are as follows: 98, 101, 100, 102, 97, 99, 100, 101, 98, 102. Assess whether this dataset can be reasonably assumed to follow an approximate normal distribution. In your response, calculate the mean and sample standard deviation, comment on […]
Advanced t-Interval Computation
A quality control engineer is testing the consistency of a manufactured component. A sample of 15 measurements from components produced in a day was recorded, yielding a sample mean of 20.5 mm and a sample standard deviation of 1.2 mm. Construct a 95% confidence interval for the true mean measurement of the component. Assume that […]
Assessing Association with Spearman’s Rank Correlation
Explain why Spearman’s rank correlation coefficient is often preferred over Pearson’s correlation coefficient when analyzing the relationship between two variables, particularly when dealing with ordinal data or data that does not follow a normal distribution.