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Over 5000 students were tested on their abilities in Calculus and Physics for a study performed by the Third International Mathematics and Science Study. The testing was separated into four regions of the United States. Some students took the Calculus test, some took the Physics test, and some took both. Assume that the scores represent a random sample for each of the four regions of the U.S.

Test the claim made by Physics teachers that the overall mean U.S. score on the Physics test should be higher than 420. Use a significance level of α = 0.05.

Lee Creighton (modified by Paris Faison)
SAS Institute

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The Scores data set contains the scores on a Calculus and a Physics test given to 1000 students in a particular region of the U.S.

These are the variables in the data set:

Sall, J., Creighton, L., & Lehman, A. (2006). JMP Start Statistics, Third Edition. Cary, NC: SAS Institute Inc.

The p-value for our one-sided test (given by SAS Enterprise Guide) with alternative hypothesis H_a: μ > 420, is .09375. This outcome is not significant at the α = 0.05 level. Thus we can conclude that there is not enough evidence to suggest that the data support the claim that the overall U.S. score on the Physics test should be higher than 420.

An agricultural company interested in cutting down the time needed to harvest its crops hired a mechanical engineer to design a mechanical harvester for bell peppers. To heighten the precision of his machine, the engineer measured and recorded the angle at which peppers hang on the plant.

Perform a one-sample t-test to determine whether the data gives good evidence that peppers hang on plants at an angle (different from zero).

SAS Institute Inc.

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The Peppers data set contains data about the angle at which peppers hang on the plant.

These are the variables in the data set:

This data is sample data from SAS Institute Inc.

You’re testing the following hypotheses:

H_o: μ =0  versus  H_a: μ ≠ 0,
where μ is the mean angle at which bell peppers hang.

The p-value of 0.0037 is less than .05, so there is sufficient evidence to reject the null hypothesis.  Thus, you can conclude that bell peppers hang on plants at an angle.