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Let x be the growth of a tumor over 15 days, in millimeters. Suppose this growth

ID: 3219223 • Letter: L

Question

Let x be the growth of a tumor over 15 days, in millimeters. Suppose this growth is normally distributed. You suspect the mean of the growth is 4.00 mm. You measure n = 9 such tumors and get a sample mean of bar X = 4.3 and sample standard deviation of S = 1.2. You wish to test at a level of significance a = .01. a) Write out the null hypothesis H_0 and the alternative hypothesis H_a. b) Is this a one-sided or two-sided test? c) Find the critical region for the test statistic t. d) Compute the test statistic t. e) What is your conclusion about the test? f) Find the p-value.

Explanation / Answer

(a) Ho: = 4 versus Ha: 4

(b) Two-sided test

(c) = 0.01

Degrees of freedom = 9 - 1 = 8

Lower Critical t- score = -3.355387331

Upper Critical t- score = 3.355387331

Critical region is the region to the left of t = -3.355 and to the right of 3 355

(d) SE = s/n = 1.2/9 = 0.4

t = (x-bar - )/SE = (4.3 - 4)/0.4 = 0.75

(e) Since 0.75 < 3.355, we fail to reject Ho

There is no sufficient evidence that 4

(f) p- value = 0.474731185