Suppose that we wish to test H0: suppose that a sa of x 35 a Calculate the value

Question

Suppose that we wish to test H0: suppose that a sa of x 35 a Calculate the value of the test statistic z. b By comparing z with critical values, test Ho versus Ha at c Calculate the p-value for testing Ho versus H d Use the p-value to test Ho versus H, at each of = .10, .05, .01, and .001 e How much evidence is there that Ho: = 40 is false and H, 40 is true? 0.12 40 versus H : 40, where i s known to equal 18. Also, mple of n - 81 measurements randomly selected from the population has a mearn -05.

Explanation / Answer

Question 9-12

H0 : = 40

Ha :    40

(a) standard error of sample mean se0 = /sqrt(n) = 18/ sqrt(81) = 2

Here sample mean x = 35

Z = (x - 40)/ se0 = (35 - 40)/ 2 = -2.5

(b) Here critical value of Z at alpha = 0.05 is Z = +- 1.96

so here Z > Zcritical

(c) p - value = 2 * Pr(Z < -2.5) = 2 * 0.00621 = 0.0124

(d) at alpha= 0.10 ; we reject the null hypothesis .

at alpha = 0.05 ; we reject the null hypothesis .

at alpha = 0.01; we cannot reject the null hypothesis.

at alpha = 0.001; we cannot reject the null hypothesis.

(e) There is significant evidence of at least 0.01 level that null hypotheiss is false and alternative hypotheiss is true

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