Same as the previous except this is two-tailed test.

μ=100    s=10    n=30    H0:μ=100    Ha:μ≠100    "Ha ≠ H0"   Two-tailed test.
x̄	t	crit α=.05	crit α=.01	p	Reject H0 ?
102					.05 .01
103					.05 .01
104					.05 .01
105					.05 .01

Compared with a one-tailed test, two-tailed tests the p-value, making it to reject H₀.
Do one-tailed vs two-tailed make a difference in the value of the test statistic t?
Two-tailed tests make the critical values than the critical values for one-tailed tests.

Effect of larger sample size n.

μ=100    s=10    n=100    H0:μ=100    Ha:μ>100    "Ha > H0"   Right-tailed test.
x̄	t	crit α=.05	crit α=.01	p	Reject H0 ?
102					.05 .01
103					.05 .01

μ=100    s=10    n=100    H0:μ=100    Ha:μ≠100    "Ha ≠ H0"   Two-tailed test.
x̄	t	crit α=.05	crit α=.01	p	Reject H0 ?
102					.05 .01
103					.05 .01

Notice that these only need to get to x̄=103 before rejecting the null hypothesis that μ=100.
The larger sample size n enables finding smaller differences that are significant.

Effect of smaller s.   (with n=30)

μ=100    s=5    n=30    H0:μ=100    Ha:μ>100    "Ha > H0"   Right-tailed test.
x̄	t	crit α=.05	crit α=.01	p	Reject H0 ?
102					.05 .01
103					.05 .01

Effect of smaller s.

μ=100    s=5    n=30    H0:μ=100    Ha:μ≠100    "Ha ≠ H0"   Two-tailed test.
x̄	t	crit α=.05	crit α=.01	p	Reject H0 ?
102					.05 .01
103					.05 .01

Compared to the original (s=10, n=30) tests, having less variation in the population and thus a smaller s, makes the test statistic t more extreme and thus we are more likely to reject the null hypothesis.