Question

what is the hypothesis for

1. one-sample t test, dependent samples t test, independent samples t test.

Answer 1

One sample t test is the test for single mean , where we test whether the population mean takes the specified value . The null hypothesis is the hypothesis of no difference , thus null hypothesis is of the form

H0 : $\mu =\mu _{0}$

where $\mu _{0}$ is the specified value of mean

The alternative hypothesis can be non directional given by

$Ha:\mu \neq \mu _{0}$

then the test is two tailed.

or one directional given by

$Ha:\mu > \mu _{0}$ ( right tailed test )

or

$Ha:\mu < \mu _{0}$ (left tailed test )

Dependent  sample t test is the test for difference between two means , we use the test when we have dependent or related samples , such as two sets of observation on same set of subjects at two different times or cimcumstances . The null hypothesis is the hypothesis of no difference ,that is difference between two means is zero, thus null hypothesis is of the form

$H0:\mu_{d} =0$

where $\mu _{d}$ is the difference between two means  

The alternative hypothesis can be non directional given by

$Ha:\mu_{d} \neq 0$

then the test is two tailed.

or one directional given by

$Ha:\mu_{d} > 0$ ( right tailed test )

or

$Ha:\mu_{d} < 0$ (left tailed test )

Inependent  sample t test is the test for difference between two means , we use the test when we have two independent samples , . The null hypothesis is the hypothesis of no difference ,that is there is no difference between two means ,, thus null hypothesis is of the form

$H0: \mu _{1}=\mu _{2}$

where $\mu _{1}$ and $\mu _{2}$ are two population means

The alternative hypothesis can be non directional given by

$Ha: \mu _{1}\neq \mu _{2}$

then the test is two tailed.

or one directional given by

$Ha: \mu _{1}> \mu _{2}$ ( right tailed test )

or

$Ha: \mu _{1}< \mu _{2}$ (left tailed test )