Question

Use Random number generator (under Data Analysis) to simulate the following data set. Create 10 columns, each 20 points long and use the following parameters: Number of variables (10), number of data point (20), Distribution (Normal), Mean (40), Standard Deviation (10), Random seed (1234). The data should be in columns: A,B,C,….,I,J. Randomly pick two columns (say Column B and Column H) and perform 2-sided t-test on these two data columns. Record the P-value and repeat this procedure several times (at least 5 times). That is, each time randomly pick two columns, perform 2-sided t-test and record the P-value. And answer the questions. (Pick the closest answer) 17. What did you observe? a. Most of the P-values are very small, and some below 5%. b. P-values are very different, some small and some large, but very few, if any, below 5% c. Most of the P-values are very large, around 0.9 and 0.95 range. d. ​​Essentially all P-values are below 5% and some even below 1% range. 18. What is the Statistical interpretation? a. Since data are created randomly one expect to see small P-value for t-test. b. The t-test worked as designed, since in most cases it detected the difference, sometimes even with 1% threshold. c. The t-test worked as designed, in most cases it did not detect the difference since the data are created with equal means (equal averages). d. None of the above Create one more random column of data. This time use the following parameters: Number of variables (1), number of data point (20), Distribution (Normal), Mean (50), Standard Deviation (10), Random seed (3434). CUT &PASTE this data in the same sheet as the previous 10 columns and put it in column M. Randomly pick one column out of A,B,…,J (say Column F) and perform 2-sided t-test based on this randomly picked column and the newly created column M. Record the P-value and repeat this procedure several times (at least 5 times). That is, each time randomly pick one data from the ten previously created and perform 2-sided t-test versus the newly created column M. Record the P-value. And answer the questions. (Pick the closest answer) 19. What did you observe? a. Most of the P-values are very small, and some below 5%. b. P-values are very different, some small and some large, but very few, if any, below 5% c. Most of the P-values are very large, around 0.9 and 0.95 range. d. Essentially all P-values are below 5% and some even below 1% range. 20. What is the Statistical interpretation? a. Since data are created randomly one expect to see small P-value for t-test. b. The t-test worked as designed, since in most cases it detected the difference, sometimes even with 1% threshold. c. The t-test worked as designed, in most cases it did not detect the difference since the data are created with equal means (equal averages). d. None of the above

Answer 1

ANSWER:

'Given that,

17)

option B is correct.

18)

option C is correct.

part -2:

> set.seed(3434)
> M = rnorm(20,50,10)
> M
[1] 45.93904 35.87163 60.34832 44.38388 49.84033 49.61631 48.19858 46.23254 46.82688 67.83189 62.74389 50.82694 50.86437 57.84251 68.30389 28.44567 51.51725 44.33325 37.06757 47.23892

T-Test:

> t.test(A,M)

Welch Two Sample t-test

t = -4.3517, df = 19.384, p-value = 0.0003296

> t.test(I,M)

Welch Two Sample t-test

t = -4.1386, df = 19.497, p-value = 0.0005327

> t.test(F1,M)

Welch Two Sample t-test

t = -4.3046, df = 19.142, p-value = 0.0003767

> t.test(D,M)

Welch Two Sample t-test

t = -4.1123, df = 19.425, p-value = 0.0005699

> t.test(H,M)

Welch Two Sample t-test

t = -4.1446, df = 19.247, p-value = 0.0005379

19)

option D is correct.

20)

option B is correct.