1. Explain the difference between a z-statistic and a t-statistic. When might you use one or the other?
2. List the four measurement scales. Which scales are used for qualitative data and which scales are used for quantitative data?

 

1. Z-statistic can be used to compare population means to a sample's. The z-score tells you how far, in standard deviations, a data point is from the mean or average of a data set. A z-statistic compares a sample to a defined population and is typically used for dealing with problems relating to large samples (n > 30). Z-statistics can also be helpful when we want to test a hypothesis. They are most useful when the standard deviation is known.

T-statistic are used to test a hypothesis, but they are most useful when we need to determine if there is a statistically significant difference between two independent sample groups. A t-statistic asks whether a difference between the means of two groups is unlikely to have occurred because of random chance. T-statistics are most appropriate when dealing with problems with a limited sample size (n < 30).

2. The measurement scales are four in number, namely;

Nominal scale- is a scale of measurement that is used for identification purposes. It is the coldest and weakest level of data measurement among the four.

Ordinal scale- involves the ranking or ordering of the attributes depending on the variable being scaled. The items in this scale are classified according to the degree of occurrence of the variable in question.

Interval scale- is a scale in which the levels are ordered and each numerically equal distances on the scale have equal interval difference. If it is an extension of the ordinal scale, with the main difference being the existence of equal intervals

Ratio scale- is the peak level of data measurement. It is an extension of the interval scale, therefore satisfying the four characteristics of measurement scale; identity, magnitude, equal interval, and the absolute zero property.

With nominal and ordinal scale being used to measure qualitative data, while interval and ratio scales are used to measure quantitative data.