Test the following hypotheses against two-sided alternatives using the given information. In the following, Xn is the

Question:

Test the following hypotheses against two-sided alternatives using the given information.

In the following, Xn is the sample mean, s

³

Xn

´

is its standard error, s2 is the sample variance, n the sample size, and ¹ Æ E[X].

(a) H0 : ¹ Æ 0, Xn Æ 1.2, s

³

Xn

´

Æ 0.4.

(b) H0 : ¹ Æ 0, Xn Æ ¡1.6, s

³

Xn

´

Æ 0.9.

(c) H0 : ¹ Æ 0, Xn Æ ¡3.5, s2 Æ 36, n Æ 100.

(d) H0 : ¹ Æ 1, Xn Æ 0.4, s2 Æ 100, n Æ 1000.

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