Class 2 Hypothesis Test for p Hypothesis Test

A Population Proportion, p • Population is characterized by objects that possess or do

Proportions (cont. ) • The problem is analogous to the problem about means. •

EXCEL and Population Proportions • EXCEL does not directly support the computation that we

Tests for when is Unknown: The t-test • Situation is the same as before:

Doing a t-test in EXCEL • Use tools/data analysis/t-Test: Paired Two Sample for Means.

Comparing Two Population Means • Hypothesis consists of a direct comparison (by looking at

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Class 2 Hypothesis Test for p Hypothesis Test for --Small sample, unknown Hypothesis Test for 1 - 2 (large sample)

A Population Proportion, p • Population is characterized by objects that possess or do not possess some attribute. We are interested in the proportion of the population that has the attribute. • • • Proportion of voters that will vote for a party. Proportion of smokers that contract a disease. Proportion of defects shipped in a manufactured lot. Proportion of invoices which contain an error. Proportion of consumers who will buy a product.

Proportions (cont. ) • The problem is analogous to the problem about means. • Here we have a population proportion, p, that we do not know. We will take a sample and compute the sample proportion, . It turns out that under repeated sampling, has a normal distribution with • Thus, we will be able to construct a test statistic

EXCEL and Population Proportions • EXCEL does not directly support the computation that we are doing. • Two possible approaches: • (1) Use the z-test. The mean (X) to test is the hypothesized value of p. The standard deviation is your computation of. For a sample of size n, put the value of in n consecutive cells. • (2) Use the function critbinom(n, p, ).

Tests for when is Unknown: The t-test • Situation is the same as before: we want to test a hypothesis about a population mean. This would lead us to use our test statistic • But what would we do if we don’t know ? As you might already guess, this is the rule as opposed to the exception. Thus, our test has wide applicability.

Doing a t-test in EXCEL • Use tools/data analysis/t-Test: Paired Two Sample for Means. • Input data as normal, but input a new data set of 0’s of the same size. • The hypothesized difference is just the hypothesized mean.

Comparing Two Population Means • Hypothesis consists of a direct comparison (by looking at a difference) of 1 and 2. • Directly supported by EXCEL through tools/data analysis/z-Test: Two sample for means.