Mutple choice crcse the one best answer 1 The man objecive of hycothesis testing

Question

Mutple choice crcse the one best answer 1 The man objecive of hycothesis testing is to determine which of two statements concerring a a sample staistic is re b a sample statstc is more Ikety d a population parameter is more isely 2 Which of the tolowing statements could serve as an sltermative typotfess? a X-bar 13 3 Far a hypothwsis test wth a twed levei of signticance (as what wh happen crease the sample size of the errar ul) if we to te probabity of a Type test? a Bwll increase b pwil decrease wt not change d we cannot determine what wil happen We have eeated a 96% confidence nterval for ? and t is (83.6 to 91.4 What conclusion wil e make if we test Ho ?-84 vs. Ha .. 84 at a level of significance of a 04? a. fal 1o reject Ho b accept Ho as a true stalement c reject Ho (Ha is more Ikeiy) d we ane unabic to tel what the resut wil be 5 Suppose the p-value for ana 01 hypothesis sest is calculated to be 04 interpret thhs result a there is sutficient evidence to reject Ho b. the probabiity of rejeting Ho s 04 c. the probablty that Ho is correct is .96 d. there is insutcient evidence to reject Ho

Explanation / Answer

1) The main objective of hypothesis is to determine which of two statements concerning a population parameter is true. Hence option (c) is correct.

2) Alternative hypothesis is a statement about a population parameter which does not contain '=' sign. Here options (a) and (d) are statements about sample parameters and (b) contains an '=' sign. Hence option (c) is correct.

3) Decreasing the sample size makes the hypothesis test less sensitive. This reduces the power of the test and hence increases the type 2 error (which is equal to 1- power). Hence option (a) is correct.

4) Since 96% confidence interval for mean (?) is (83.6,91.4), we are 96% confident that the mean will lie in this interval. Since ?= 84 lies in this interval, we can say with 96% confidence that ?=84. Hence we fail to reject H0 at ?=.04 . Hence option (a) is correct.

5) We reject null hypothesis at ? level of significance if p-value < ?. Since

p-value (.04) > ? (.01) , there is insufficient evidence to reject H0 . Hence option (d) is correct.  

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