Question

Use Random number generator (under Data Analysis) to create THREE columns of data each 20 points long.

-For the FIRST data set use the following parameters: number of variables (2), number of data point (20), Distribution (Normal), Mean (20), Standard Deviation (5), Random seed (1234). Keep these data in columns labeled A and B.

-For the SECOND data set use the following parameters: number of variables (1), number of data point (20), Distribution (Normal), Mean (30), Standard Deviation (5), Random seed (7767). Cut and paste this data into column C, next to the data earlier created.

Perform two t-tests, one comparing data in columns A and B and the other comparing the data in columns A and C. And answer the questions. (Pick the closest answer)

13. The two P-values are:

a. Both smaller than 5% but larger than 1%

b. Both smaller than 1%

c. One smaller than 1% and one larger than 1%

d. Both larger than 5%

14. What is the Statistical interpretation for these two t-test?

a. Since both P-values are small in both cases we have a conclusive answer.

b. In one case we have a conclusive answer while for other we do not.

c. Both P-values are too large and we can conclude that the two averages are the same.

d. None of the above

15. What is the conclusion?

a. Statistical interpretation agrees with the intuition: the data in Column C is created with the mean of 30 which is different from 20, and one of the t-tests detected this difference.

b. The statistics does not agree with the intuition: the new data is created with different means and yet, the statistics yields inconclusive statement.

c. The P-value is very small and we can conclude that the correlation between the data is significant.

d. None of these

Answer 1

We first write the R program

rm(list=ls(all=TRUE))
set.seed(1234)
A=rnorm(20,20,5)
B=rnorm(20,20,5)
set.seed(7767)
C=rnorm(20,30,5)
TAB=t.test(A, B, alternative = "two.sided", var.equal = TRUE)
TAB

Two Sample t-test

data: A and B
t = 1.1349, df = 38, p-value = 0.2635
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-1.279120 4.543179
sample estimates:
mean of x mean of y
18.74668 17.11465

TAC=t.test(A, C, alternative = "two.sided", var.equal = TRUE)
TAC

Two Sample t-test

data: A and C
t = -5.8991, df = 38, p-value = 7.829e-07
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-14.444723 -7.063713
sample estimates:
mean of x mean of y
18.74668 29.50090

13. The two P-values are : One smaller than 1% and one larger than 1%

14. The Statistical interpretation for these two t-test is says that in one case we have a conclusive answer while for other we do not.

15. The conclusion is that statistical interpretation agrees with the intuition: the data in Column C is created with the mean of 30 which is different from 20, and one of the t-tests detected this difference.