1 sample t-test Flashcards
Dr. Angela Rowson is an Educational Psychologist and is particularly interested in ADHD in school children. Using motion capture technology (i.e. infra red tracking of reflective markers attached to the head and shoulders) she has devised a method to measure the ability of a child to stay still while undertaking an engaging video game task. This method recovers a single variable (in metres) which is related to the amount of movement the child exhibits during a 5 minute video game task - Angela calls this variable the move score.
Angela wants to test the hypothesis that move scores for these children with an ADHD diagnosis will be significantly higher than 0. This is equivalent to suggesting that the sample of data obtained has come from a distribution with population mean equation image indicator> 0.
The data for the 10 children are given below
{0.09, 0.41, 0.02, 0.90, 0.07, 0.26, 0.23, 0.13, 0.15, 0.05}
Use a 1 sample t-test to test Angela’s hypothesis and pick the answer which most accurately reflects how this test should be reported.
Hint 1: The sample mean and s.d. for these 10 children are 0.2310 and 0.2625 respectively
Hint 2: The hypothetical population mean from which you are testing for departure is 0.
a. t = 2.7831, p < 0.025 Angela should reject the null hypothesis in favour of the 1-tailed research hypothesis. More specifically, she has evidence that the sample of movement scores she has from children with an ADHD diagnosis comes from a population with mean higher than 0. b. t = 2.7831, p < 0.01 Angela should reject the null hypothesis in favour of the 1-tailed research hypothesis. More specifically, she has evidence that the sample of movement scores she has from children with an ADHD diagnosis comes from a population with mean higher than 0. c. t = 0.88, p > 0.05 Angela should fail to reject the null hypothesis . More specifically, she does not have evidence that the sample of movement scores she has from children with an ADHD diagnosis comes from a population with mean higher than 0. d. t = 2.7831, p < 0.05 Angela should reject the null hypothesis in favour of the 1-tailed research hypothesis. More specifically, she has evidence that the sample of movement scores she has from children with an ADHD diagnosis comes from a population with mean different from 0.
1) Find t-score
sample mean = 0.2310
sample s.d. = 0.2625
e.s.e. = sample s.d. / SQRT sample size
e.s.e. = 0.2625 / SQRT 10
e.s.e. = 0.083
t score = (x - sample mean) / e.s.e.
t score = (0 - 0.2310) / 0.083
t score = -2.7831
2) Find the probability
v = N -1
v = 10 - 1
v = 9
Table shows tha v =9:
5% = 1.833
2.5% = 2.262
1% = 2.821
0.5% = 3.250
Which t-score is closest to 2.7831?
2.5% = 2.262
1% = 2.821
Probability =
p < 0.025 ////////
p > 0.01
3) Fail to reject or reject H0
We reject the null hypothesis because p < 0.025
ANSWER = A
Visiting aliens from Ziltoidia 10 are very worried about their hair growth on earth. Traditionally Ziltoidian hair is shaved on top and as long as possible around the sides and back. Ziltoidians are very proud of their ability to grow their hair quickly and it is known that on Ziltoidia 10, the population mean hair growth rate is an impressive 1.0 cm/day. Due to the differences between earth’s atmosphere and that of Ziltoidia 10, they are concerned that their hair will grow at a different speed here relative to their home planet. The Ziltoidian leader asks you to conduct a statistical test to assess hair growth rate in a sample of 25 Ziltoidians and report back on whether it is different from back home.
You formulate a research hypothesis: Ziltoidian hair growth rate will differ on earth from that on Ziltoidia 10. More specifically you propose that the sample of growth rate data comes from a population with mean equation image indicator ≠ 1.0 cm/day.
You also measure the average rate of hair growth in each member of the sample over a period of 30 days. The sample mean and s.d. for hair growth rates over the 25 Ziltoidian participants are 0.965 cm/day and 0.1 cm/day respectively.
Conduct the appropriate t-test to test this hypothesis and select the best summary of the outcome from the options below.
a. t = -1.75, p > 0.05. We failed to reject the null hypothesis. We can conclude that Ziltoidian hair growth rate is the same on earth to that on Ziltoidia 10. b. t = -0.35, p > 0.05. We failed to reject the null hypothesis. We do not have evidence to suggest that Ziltoidian hair growth rate is different on earth to that on Ziltoidia 10. c. t = -1.75, p < 0.05. We can reject the null hypothesis. We have evidence to suggest that Ziltoidian hair growth rate is less on earth to that on Ziltoidia 10. d. t = -1.75, p > 0.05. We failed to reject the null hypothesis. We do not have evidence to suggest that Ziltoidian hair growth rate is different on earth to that on Ziltoidia 10.
1) Find t-score
sample mean = 0.965
sample s.d. = 0.1
e.s.e. = sample s.d. / SQRT sample size
e.s.e. = 0.1 / SQRT 25
e.s.e. = 0.02
t score = (x - sample mean) / e.s.e.
t score = (1.0 - 0.965) / 0.02
t score = 1.75
2) Find the probability
v = N -1
v = 25 - 1
v = 24
Table shows that v =24:
5% = 1.711
2.5% = 2.064
1% = 2.492
0.5% = 2.797
Which t-score is closest to 1.75?
5% = 1.711
2.5% = 2.064
Probability =
p > 0.05 ////////
p < 0.01
3) Fail to reject or reject H0
We fail to reject the null hypothesis because
p > 0.05
ANSWER = D
