2. According to the hypothesis, sample size, and test statistic, i) find the reject region, ii) critical value, then iii) estimate p value from the t-table, finally iv) state the conclusion for the following case, when α=0.05

a. Ho: μ=5, Ha: μ>5
Sample size is 17, ts= 1.4,

b. Ho: μ=5, Ha: μ≠5
Sample size is 16, ts= 4,

c. Ho: μ=0, Ha: μ≠0
Sample size is 12, ts= -1,

d. Ho: μ=5, Ha: μ<5
Sample size is 10, ts= 2,

e. Ho: μ=5, Ha: μ<5
Sample size is 10, ts= -0.5


3. A dendritic tree is a branched structure that emanates from the body of a nerve cell. In a study of brain development, researchers examined brain tissue from 36 adult guinea pigs. The investigators randomly selected nerve cells from a certain region of the brain and counted the number of dendritic branch segments emanating from each selected cell. A total of 36 cells (1 per pig) was selected, and the resulting counts were as follows:
measurements
28 24 38 25
42 26 29 45
25 26 49 28
35 47 26 31
35 28 41 46
33 24 26 32
48 35 35 39
53 38 38 59
17 26 44 53

Perform a hypothesis test to address the questions. Define the Ho and Ha, compute the test statistic, define the reject region, estimate the p-value and then state the conclusion.

a) Is the mean number of cells is different from 37?
b) Is the mean number of cells is greater than 38?