Question

Please do work by hand (not in R) and show enough work so I can understand how to do it myself. Thanks.

1. The data in Table 3.3 are a subset of the data obtained by Kaneto, Kosaka, and Nakao (1967). The experiment investigated the effect of vagal nerve stimulation on insulin secretion. The subjects were mongrel dogs with varying body weights. Table 3.3 gives the amount of immunoreactive insulin in pancreatic venous plasma just before stimulation of the left vagus nerve (x ) and the amount measured 5 min after stimulation (y) for seven dogs. Test the hypothesis of no effect against the alternative that stimulation of the vagus nerve increases the blood level of immunoreactive insulin. Table 3.3 Blood Levels of Immunoreactive Insulin ( μ U/ml) Dog i , | Y, 1350480 2 200 130 3 240 250 4 290 310 5 90280 6 370 1450 7240 280

Answer 1

First, let's solve this by framing null and alternate hypothesis,

The null hypothesis which is H₀ => $\mu$_before  - $\mu$_after = 0

The alternate hypothesis on the other hand is H₁ => $\mu$_before - $\mu$_after <0

1)The mean of the first sample i.e., before the stimulation $\mu$_before =254 And standard deviation SD_before =95

2)The mean and SD of the second sample are $\mu$_after = 454, SD_after = 451

Now let's proceed to the pooled t-test to test our hypothesis

3)Let us assume that level of significance $\alpha$ = 0.05

4) compute the t-statistic

S_p= $\sqrt{\frac{(6*95^2&plus;6*451^2)}{7&plus;7-2}}$

==> S_p = 326

t^*  =$\frac{x1-x2}{sp\sqrt{\frac{1}{n1}&plus;\frac{1}{n2}}}$

= -1.15

Lets calculate the t critical, t critical at $\alpha$ = 0.05 and DOF = 12 is, -1.78 from the table for a left tailed test.

Since t^* > t criticle, we accept the H_0, Therefore, there is no much difference due to the simulation