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Using Excel:

Hypothesis Tests with Two Samples

We will consider the differences between two population means using software (Excel here). Generally withany software we are really looking for P-values. So, deciding to support the claim or not will be based entirelyon the P-value. This way, you dont really need to specify a significance level at the beginning of each test

You just run the test and check for significance by inspecting the P-value.The data is for the cholesterol levels for men diagnosed with high cholesterol. The first row comes from

men who had no treatment and the second from men who used a certain cholesterol lowering drug. We wantto test claims about how effective the drug is. With software, you dont have to calculate differences, meansvariances, or standard deviations, the software will calculate what it needs.

Cholesterol Levels in mg/dLNo Drug 237 289 257 228 303 275 262 304 244 233

Drug 194 240 230 186 265 222 242 281 240 212

Paired Data

Lets assume that the data represents the cholesterol levels for each of 10 men in the sample, before andafter using the drug. This type of data is called matched pairs. We will use Excels t-test for paired twosample means. This is found in the Data Analysis ToolPak. Below I demonstrate two such t-tests for twohypothesized mean differences between the populations.

Process:

(1) Click on the Data Analysis tab and chooset-Test: Paired Two-Sample For Means.(2) Input the data with the first sample being theone with the greater mean.(3) Enter a hypothesized mean difference.(4) Click on OK(5) Results

Conclusions:

(1) At the 0.01 significance level there is sufficient

sample evidence to support the claim that the drugreduces cholesterol levels in all men.

(1) At the 0.05 significance level there is suffi-cient sample evidence to support the claim thatthe drug reduces cholesterol levels by more than 20mg/dL.

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Independent Data

In this section we will assume the data came from two different populations of men; those who used thedrug and those who did not. We will use Excels t-test for two sample means. This is found in the DataAnalysis ToolPak. Below I demonstrate two such t-tests for two hypothesized mean differences between thepopulations.

Process:

(1) Click on the Data Analysis tab and chooset-Test: Two-Sample Assuming Unequal Variances.(2) Input the data with the first sample being theone with the greater mean.(3) Enter a hypothesized mean difference.(4) Click on OK(5) Results

Conclusions:

(1) At the 0.01 significance level, there is notsufficient sample data to support the claim thatthe mean cholesterol level for men who use thedrug is less than the mean for those who do notuse the drug.

(2) At the 0.05 significance level, the sam-ple data supports the claim that the meancholesterol level for men who use the drug is

below the mean for those who do not use the drug.

(3) At the 0.05 significance level, the sam-ple data supports the claim that the meancholesterol level for men who use the drug is morethan 5 mg/dL below the mean for those who donot use the drug.

Observation

A claim is generally easier to support if the data comes in pairs. Or, differences are more significant i

they come from pairs. This is because the variations between the two populations is less.