Question

If n=35, t=2.07, what is the p-value?

If z = -1, what is P(z > -1)?

If z = -1, what is P(z < -1)?

If x = 30 and n = 200, what is the proportion?

Answer 1

Solution:

Part i) If n=35, t=2.07, what is the p-value?

We need to use Excel command to get exact p-value and we assume this is two tailed test, since it is not mentioned:

=T.DIST.2T( t value , df)

where t = 2.07 and df = n - 1 = 35 - 1 = 34

Thus

=T.DIST.2T( 2.07 , 34)

=0.04612

Thus p-value = 0.04612

( If this is one tailed test, then p-value = 0.0461 / 2 = 0.02306 )

Part ii) If z = -1, what is P(z > -1)?

P(z > -1) = 1 - P( Z < -1)

Look in z table for z = -1.0 and 0.00 and find area.

P( Z < -1.00 ) = 0.1587

thus

P(z > -1) = 1 - P( Z < -1)

P(z > -1) = 1 - 0.1587

P(z > -1) = 0.8413

Part iii) If z = -1, what is P(z < -1)?

P(z < -1) = ...?

From part ii) we have P( Z< -1.00) = 0.1587

Thus

P(z < -1) = 0.1587

Part iv) If x = 30 and n = 200, what is the proportion?

Thus proportion is: