In a one-tailed test, the alternative hypothesis contains the less than (“<“) or greater than (“>”) sign. This indicates that we’re testing whether or not there is a positive or negative effect.
Check out the following example problems to gain a better understanding of one-tailed tests.
Suppose it’s assumed that the average weight of a certain widget produced at a factory is 20 grams. However, one engineer believes that a new method produces widgets that weigh less than 20 grams.
To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses:
To test this, he uses the new method to produce 20 widgets and obtains the following information:
Plugging these values into the One Sample t-test Calculator, we obtain the following results:
Since the p-value is not less than .05, the engineer fails to reject the null hypothesis.
He does not have sufficient evidence to say that the true mean weight of widgets produced by the new method is less than 20 grams.
Suppose a standard fertilizer has been shown to cause a species of plants to grow by an average of 10 inches. However, one botanist believes a new fertilizer can cause this species of plants to grow by an average of greater than 10 inches.
To test this, she can perform a one-tailed hypothesis test with the following null and alternative hypotheses:
Note: We can tell this is a one-tailed test because the alternative hypothesis contains the greater than (>) sign. Specifically, we would call this a right-tailed test because we’re testing if some population parameter is greater than a specific value.
To test this claim, she applies the new fertilizer to a simple random sample of 15 plants and obtains the following information:
Plugging these values into the One Sample t-test Calculator, we obtain the following results:
Since the p-value is less than .05, the botanist rejects the null hypothesis.
She has sufficient evidence to conclude that the new fertilizer causes an average increase of greater than 10 inches.
A professor currently teaches students to use a studying method that results in an average exam score of 82. However, he believes a new studying method can produce exam scores with an average value greater than 82.
To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses:
Note: We can tell this is a one-tailed test because the alternative hypothesis contains the greater than (>) sign. Specifically, we would call this a right-tailed test because we’re testing if some population parameter is greater than a specific value.
To test this claim, the professor has 25 students use the new studying method and then take the exam. He collects the following data on the exam scores for this sample of students:
Plugging these values into the One Sample t-test Calculator, we obtain the following results:
Since the p-value is less than .05, the professor rejects the null hypothesis.
He has sufficient evidence to conclude that the new studying method produces exam scores with an average score greater than 82.
The following tutorials provide additional information about hypothesis testing:
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike. My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
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