In one sample t-test, we seek to compare the sample mean with the hypothesized mean. But I want to know if it is possible to calculate this statistics without a hypothesized mean using SPSS?
Its not really clear to me what you are trying to achieve, and if a one-sample t-test is at all useful.
The whole purpose of the one-sample t-test is to compare a sample mean to a null-hypothesis (population) mean. The one sample t-test only meaningfully deviates from a z-test in that variance in the population is assumed to be unknown. This means that in the numerator you will always have:
X - Mu.
You therefore need some kind of Mu. This can be anything really, but it needs to be something. You can't leave it out, the one-sample t-test equation absolutely needs a value for Mu.
It is important to note that the Mu-parameter is not so much a hypothesised mean, but a **null**-hypothesised mean. Maybe this already helps you with formulating a null-hypothesis (population) value to compare your sample mean to.
If you don't really have an intention to compare your sample mean to anything in particular, it sounds like it would suffice to just provide the sample mean (and variance/standarddeviation) without further hypothesis testing?
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