Boston University School of Public Health

Sample question: A researcher claims that more than 23% of community members go to church regularly. In a recent survey, 126 out of 420 people stated they went to church regularly. Is there enough evidence at α = 0.05 to support this claim? Use the P-Value method to support or reject null hypothesis.

Quantitative Response Variables and Means

The is the one you would believe if the null hypothesis is concluded to be untrue. The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a -value to weigh the strength of the evidence (what the data are telling you about the population). The -value is a number between 0 and 1 and interpreted in the following way:


Null and Alternative Hypotheses for a Mean

where μ0 = 2 ppm is the allowable limit and μ is the population mean of the measured soil ().

Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:


Sample standard deviation - the standard deviation of the sample.

Example: An advertiser claims there is a difference in the median householdincome for card holders of Visa Gold and Gold Master Card. The result of a random sampleof 100 customers from each card group are shown below:

What a p-Value Tells You about Statistical Data

The p-value is the probability that a t-value would be greater than (to the right of ) 4.03. From Minitab we get 0.001. If using we would look at DF = 9 and since t = 4.03 > 3.00 our p-value from the table would p

A confidence interval for the mean.

The critical value of Z for α =0.05 is Z = 1.645 (i.e., 5% of the distribution is above Z=1.645). With this value we can set up what is called our decision rule for the test. The rule is to reject H0 if the Z score is 1.645 or more.

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

Test statistic: The sample statistic one uses to either reject Ho (and conclude Ha) or not to reject Ho.

Alt. Hypothesis - select a two-sided test (~=) or a one-sided test.

Use the Options button to specify the hypotheses to be tested. If the P-value is less than the alpha risk which you specify, you should reject the null hypothesis at the corresponding significance level.

This tab shows the power curve for the t test:

The alternative hypothesis tells us two things. First, what predictions did we make about the effect of the independent variable(s) on the dependent variable(s)? Second, what was the predicted direction of this effect? Let's use our example to highlight these two points.