Area under the t-distribution: Using the critical values table Flashcards
As the parameter v increases, what happens to the Student’s t-distribution’s t-score and curve?
t-score = gets smaller and closer to the SND
curve = gets closer to the SND
As the parameter v decreases, what happens to the Student’s t-distribution?
t-score = gets bigger and further away from the SND
curve = gets further away from the SND
We have a sample of 6 people from a normal population.
What is the probability that the t-score will be greater than 3.0?
1) Find the parameter v
v = N-1
v = 6 -1 = 5
2) Look at the parameter v and t-score table and find v = 5
3) Table shows that v = 5 is:
5% above 3.0 = 2.015
2.5% above 3.0 = 2.571
1% above 3.0 = 3.365
0.5% above 3.0 = 4.032
4) Decide on which t-score values are the closest to 3.0 which are:
2.5% above 3.0 = 2.571
1% above 3.0 = 3.365
5) Conclude the probability that the t-score will be greater than 3.0
ANSWER = p < 0.025 but p > 0.01
You calculate a t-score from a sample mean based on a sample of size 25 from a normal population with an unknown population standard deviation. Let p be the probability that the t-score is either less than -2.15 or more than 2.15, i.e. that the sample mean is more than 2.15 e.s.e.’s away from (above or below) the population mean).
Which of the following statements correctly describes p?
a. p < 0.05 and p > 0.02 b. p < 0.025 and p > 0.01 c. This can not be calculated d. p < 0.025 and p > 0.02
1) Find the parameter v
v = N-1
v = 25 -1 = 24
2) Look at the parameter v and t-score table and find v = 24
3) Table shows that v = 24 is:
10% below or above 2.15 = 1.711
5% below or above 2.15 = 2.064
2% below or above 2.15 = 2.492
1% below or above 2.15 = 2.797
4) Decide on which t-score values are either less than -2.15 or more than 2.15
5% below or above 2.15 = 2.064
2% below or above 2.15 = 2.492
5) Conclude the probability that the t-score will be either less than -2.15 or more than 2.15
ANSWER = a. p < 0.05 but p > 0.02
What value of t isolates 1% of the area under t(20) in one tail?
a. 2.861 b. 2.539 c. 2.845 d. 2.528
1) Look at the t-score table and find t(20) or v = 20
3) Table shows that v = 20:
1% two-tailed t-value = 2.228
ANSWER = d. 2.528
You calculate a t-score from a sample mean based on a sample of size 36 from a normal population with an unknown population standard deviation. Let p be the probability that the t-score is less than -1.9 (i.e. that the sample mean is more than 1.9 e.s.e.’s below the population mean).
Which of the following statements correctly describes p?
a. This can not be calcualted. b. p > 0.05 and p > 0.025 c. p < 0.05 and p < 0.025 d. p < 0.05 and p > 0.025
1) Find the parameter v
v = N-1
v = 36 -1 = 35
2) Look at the parameter v and t-score table and find v = 35
3) Table shows that v = 35 is:
5% below or above 2.15 = 1.690
2.5% below or above 2.15 = 2.030
1% below or above 2.15 = 2.438
0.5% below or above 2.15 = 2.724
4) Decide on which t-score values are either less than -1.9 or more than 1.9
5% below or above 2.15 = 1.690
2.5% below or above 2.15 = 2.030
5) Conclude the probability that the t-score will be either less than -1.9 or more than 1.9
ANSWER = d. p < 0.05 but p > 0.025
The area under t(18) to the right of t = 2.2 is less than 0.01.
Is this statement True or False?
a. True
b. False
t = 2.2
t = 2.2%
0.01 = 1%
2.2% > 1%
ANSWER = False
What value of t isolates 5% of the area underneath t(10) in 2 tails?
a. 1.812 b. 2.228 c. 1.833 d. 2.262
1) Look at the t-score table and find t(10) or v = 10
2) Table shows that v = 10:
5% two-tailed t-value = 2.228
ANSWER = b. 2.228
You calculate a t-score from a sample mean based on a sample of size 15 from a normal population with unknown population standard deviation. Let p be the probability that the t-score is more than 2.75 (i.e. that the sample mean is more than 2.75 e.s.e.’s above the population mean).
Which of the following statements correctly describes p?
a. p > 0.01 and p > 0.05 b. p > 0.05 c. p < 0.01 and p > 0.005 d. p > 2.75
1) Find the parameter v
v = N-1
v = 15 -1 = 14
2) Look at the parameter v and t-score table and find v = 14
3) Table shows that v = 14 is:
5% above 2.75 = 1.761
2.5% above 2.75 = 2.145
1% above 2.75 = 2.624
0.5% above 2.75 = 2.977
4) Decide on which t-score values are more than 2.75
1% above 2.75 = 2.624
0.5% above 2.75 = 2.977
5) Conclude the probability that the t-score will be more than 2.75
ANSWER = c. p < 0.01 but p > 0.005
The area under t(18) to the right of t = 2.2 is less than 0.025.
Is this statement True or False?
a. True
b. False
t = 2.2
t = 2.2%
0.025 = 2.5%
2.2% < 2.5%
ANSWER = True
