Question

The data below are the healing rates of cuts (micrometers per hour) in a matched pairs experiment. The pairs are the two hind limbs of the same newt. In each pair, one limb had reduced electrical field and the other (the control) had its natural electrical field.

Newt	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Difference (control ?experimental)	1	?10	?3	3	31	?4	12	3	7	10	22	4	1	3

Is there good evidence that changing the electrical field from its natural level slows healing? Assume that all conditions for inference are met. Perform a hypothesis test. The p-value for your test is

less than 0.01

between 0.01 and 0.05

between 0.05 and 0.10

greater than 0.10

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_d< 0

Alternative hypothesis: u_d > 0

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

s = 10.5643

SE = s / sqrt(n)

S.E = 2.8234

DF = n - 1 = 14 -1

D.F = 13

t = [ (x₁ - x₂) - D ] / SE

t = 2.024

where d_i is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 13 degrees of freedom is greater than 2.02.

Thus, the P-value = 0.032.

Interpret results. Since the P-value (0.032) is less than the significance level (0.05), we have to reject the null hypothesis.

The p-value is between 0.01 and 0.05.

Hence there is good evidence that changing the electrical field from its natural level slows healing.