Question

Are the data you collected paired or independent? Explain how you know. Describe in words the hypotheses you want to test. How did you decide what the alternative hypothesis would be? State the hypotheses using the H0 and HA symbols and other appropriate symbols. (I don't want to say too much because I don't want to give away the answer!) What conditions/assumptions/requirements need to be met for this hypothesis test? Explain them, but you don't have to check them. (Bonus point opportunity: Check the conditions for the test and show your work (e.g. a graph). Explain how the conditions are met or not.) Continue on with the test, whether or not the conditions were met. Are there any unusual data values that you decided to delete from the data set? Which values and why? What is the sample size of your data set, if/after you moved pairs of data? n = _______ What is the value of the sample mean? What is the value of the sample standard deviation? Why is the standard deviation so large (or small)? What are the degrees of freedom for this hypothesis test? What significance level will you be using for this test? (Your choice!) What is the test statistic for this test? t = _____ What is the p-value for this test? Should you reject H0 or not reject H0 ? Explain how you know. Summarize the results of the test, making sure to talk about the dominant/non-dominant hands and the speed to write the names.

Data:

How many seconds did it take to write the name using your NON-DOMINANT hand?	How many seconds did it take to write the name using your DOMINANT hand?
8.8	3.6
8.61	2.59
11.21	5.4
15.66	4.07
10.67	3.95
10.9	5.53
18.18	6.03
7.5	5.2
21.17	8.02
9.19	4.62
11.94	4.11
7.46	4.26
21.54	4.85
10.82	5.52
9.42	4.59
13.23	6.02
9.92	6.04
18.39	9.96
10.54	4.58
5.27	2.3
7.66	3.31
19.03	5.53
19.03	6.14
12.32	5.33
13.22	8.21
5.01	3.16
20.38	4.84
12.5	4.1
16.41	3.88
18.92	4.51
8.88	3.78
11.66	4.5
4.84	2.36
33.4	7.05
8.88	3.78

Answer 1

1)The data collected is paired or one can say they are matched samples that is , as the time taken to write a name is matced with other although they have different measurments on the same subject. That is why they are dependent or paired samples.

2) The null and alternative hypotheses will be:- '

Same time it take to write the name using your DOMINANT hand and NON- DOMINANT hand.

Same time does not  take to write the name using your DOMINANT hand and NON- DOMINANT hand.

Here,    , that is the difference between the samples.

3) The assumptions for the t-test are:-

a) The observations must be continuous i.e. either ratio or interval .

b) The observations should be dependent '

c) The observations are normally distributed.

d) The population standard deviation is not known

4) All the assumptions are met given above and the sample size is 36

All the furthur calculations are done in R '

a) the value of the sample standard deviation is

> sd(x$V1-x$V2)
[1] 5.116954

b) The standard deviation is large, this means there is large variability bw the samples.

c) The degrees of freedom for this hypothesis test is 36-1=35.

d) The significance level will you be using for this test is 0.01

e) The test statistic for this test is  t = 9.3115.
f) The p-value for this test is 5.298e-11.

g) A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so we reject the null hypothesis.that is the time taken to write a name  about the dominant/non-dominant hands is different .