How do I Get the Test Value for One Sample T-Test?
The one sample t-test is used to test whether a sample comes from a particular population. For example, you might test the null hypothesis that a random sample of 100 children in a city comes from a population with a mean (average) blood lead level under the CDC limit of 10ug/dl. In this example, the children measured would be called a sample of size n, where n=100. The sample mean, x-bar, is the average blood lead level of all the children in the sample, and the null hypothesis mean, μ0, is 10ug/dl.
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Instructions
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1
Identify the null hypothesis of the problem, which is the statement which you are testing. For the above example, the null hypothesis is that the children in your sample come from a population with a mean blood lead level less than 10 ug/dl.
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2
Set the null hypothesis mean, μ0, to equal the known property of the hypothetical population. In the example, μ0 is 10 ug/dl.
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3
Identify the sample size, which is the number of members or items in the sample. Set the variable "n" equal to this value. In the example, n=100.
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4
Calculate the sample mean, x-bar, by adding all the values in the sample and dividing them by the sample size n. In the example, add all the blood lead levels for all the children, and obtain an average by dividing by the number of children.
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5
Calculate the standard deviation, s. The standard deviation measures the variability in the data. Start by subtracting the sample mean from each sample value, and squaring the results. Sum these up and divide by (n-1). Finally, take the square root of the result. This procedure is more simply expressed by this equation: s = ( Σ ( xi - x-bar )2 / ( n - 1 ) ) ^(1/2), where xi represents each sample value.
For each child in the example, subtract the average lead level calculated in Step 4 from the child's individual lead level, then square the result. Sum up the results for all the children, then divide by 99 (which is 100 minus 1.) Taking the square root of the result yields the standard deviation.
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6
Calculate the square root of the sample size n. In the example, this value is 10, the square root of 100.
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Plug the values you just calculated into the formula for the test value, or t-score:
t = (x-bar - μ0)/ (s / n^1/2)
The t-score is derived by subtracting the null hypothesis mean (found in Step 2) from the sample mean (calculated in Step 4), then dividing the answer by the standard deviation (calculated in Step 5), then dividing by the square root of n (calculated in Step 6).
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Tips & Warnings
t-tests may be used even when sample sizes are as small as 10.
The t-test may be used when the population standard deviation is unknown but the population is expected to follow a roughly normal (bell-shaped) distribution.
To make sure that the normality assumption is appropriate for your data, perform a normality test or visualize the data with a histogram.
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