Question

What test statistic would we use when comparing two population proportions?

What test statistic would we use when comparing observed vs. expected frequencies?

If my degrees of freedom were 7 and I am comparing observed and expected frequencies at a 0.01 level of significance. What would my critical value be?

Answer 1

Answer:

It is common to compare two quantities, like comparing two meanings. If the 2 approximate proportions are different, it's going to ensue to a difference in population or it should be due to chance. A hypothetical test helps to check whether the approximate difference in size reflects the difference in the proportions of the population.

Many different types of tests are used in statistics when comparing two population proportions (e.g. z test, chi square test, t test). If you use the Z test:

• Your sample size must be over 30. Otherwise, use the T test.
• Data points should be independent of each other. In other words, one data point is not relevant or does not affect another data point.
• Your data should be distributed normally. However, for large samples (over 30) the size does not always matter.
• Your data should be randomly selected from the population, where each item has an equal chance of being selected.
• Sample sizes should be the same if all possible.

This test is used for differences in proportion. The two-dimensional Z-test allows you to match two quantities to work out if they're the identical.

• The null hypothesis (H0) for the test is that the proportions are the same.
• The alternate hypothesis (H1) is that the proportions are not the same.

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