To compare the population mean of a normally-distributed scale-level variable to a certain fixed value
H0: The population mean of X is equal to (some test value).
H1: The population mean of X is not equal to (some test value).
H0: The population mean of X is equal to (some test value).
H1: The population mean of X is greater than / smaller than (some test value).
Note : Strictly speaking, H0 for the one-tailed tests should be written as "The population mean of X is not greater than / smaller than (some test value)", but since we don't care about the other side here, we would use the same H0 as the two-tailed test for simplicity.
You want to know if the population mean of X is equal to 10.
H0: The population mean of X is equal to 10.
H1: The population mean of X is not equal to 10.
H0: The population mean of X is equal to 10.
H1: The population mean of X is greater than 10.
Note : We conduct the above one-tailed test only if the sample mean of X is already greater than 10. Likewise, if the word "smaller than" is used in H1 above, then we conduct the one-tailed test only if the sample mean of X is already smaller than 10.
Analyze -> Compare Means -> One-Sample T Test -> Select the Test Variables (e.g., X) -> Specify the Test Value (e.g., 10) -> Click Options button to adjust the confidence interval percentage (=1-⍺) if needed
Analyses ->T-Tests -> One Sample T-Test -> Put the test variable into the Dependent Variables box. -> Under Tests, select Student’s for t-test, or Wilcoxon rank for non-parametric test -> Under Hypothesis, set the test value and select the direction of the hypotheses -> Optionally, under Additional Statistics, select the descriptive statistics or confidence intervals to be shown -> Also do the assumption checks if necessary.
Unless otherwise specified, the p-value given in the software is the two-tailed p-value. Divide it by two to get the one-tailed p-value in case of a one-tailed test.
If p<0.05 (or other significant levels), we take H1 as true, i.e., the population mean of X is not equal to the test value.
If p is not <0.05 (or other significant levels), we take H0 as true, i.e., the population mean of X is equal to the test value.
If p<0.05 (or other significant levels), we take H1 as true, i.e., the population mean of X is greater than / smaller than the test value.
If p is not <0.05 (or other significant levels), we take H0 as true, i.e., the population mean of X is equal to the test value.
Name of the test being used (one-sample t-test)
The test variable and the test value (or the hypotheses)
The t statistic
The p-value
Your conclusion of the test
Elaboration of the result in your research context