Question

obat Reader DC N5 Sum20.pdf Appendix D (2).pdf HW4_Sum20 (1).pdf x 374 134% (12 pts) A physiologist believes he has discovered a new steroid hormone that can affect the blood glucose in reptiles. In an experiment he injects turtles with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the turtles. In his sixteen experimental turtles he obtains the following levels of blood glucose {2, 1, 3, 5, 2, 1, 1, 5, 3, 2, 1, 1, 2, 1, 1,5). From previous studies of thousands of normal, un-manipulated turtles he knows that the mean (u) blood glucose level in this species of turtle (his laboratory population) is 3. Evaluate the hypothesis that this new

Answer 1

Let X: Blood glucose of turtles.

The provided sample mean is X = 2.25 and the sample standard deviation is s = 1.5275, and the sample size is n = 16. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 3 Ha: u 7 3 This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a two-tailed test is tc = 2.131. The rejection region for this two-tailed test is R= {t : |t| > 2.131} (3) Test Statistics The t-statistic is computed as follows: t X μο s/vn 2.25 - 3 1.5275/16 = -1.964

(4) Decision about the null hypothesis = Since it is observed that t = 1.964 <tc = 2.131, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.0683, and since p = 0.0683 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean u is different than 3, at the 0.05 significance level. Confidence Interval The 95% confidence interval is 1.436 < d < 3.064.
Thus there is not sufficient evidence to conclude that steroid affect the blood glucose.

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