Question

(3 points) Suppose that we are to conduct the following hypothesis test. Ho H980 H1: μ > 980 suppose that you also know that σ-: 200, n 100, 1020, and take α-: 0.01 . Draw the sampling distribution, and use it to determine each of the following A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form -oo, a is expressed (-infty, a), an answer of the form (b, oo) is expressed (b, infty), and an answer of the form (-oo, a) U (b, oo) is expressed (-infty, a)U(b, infty) B. The rejection region for the standardized test statistic: C. The p-value is D. Your decision for the hypothesis test O A. Reject H1 OB. Reject Ho O C. Do Not Reject Ho OD. Do Not Reject H

Answer 1

Given : Hypothesis : $H_0:\mu=980$ Vs $H_1:\mu>980$

A. The standardized test statistic is ,

$Z=\frac{\bar{X}-\mu_0}{\sigma/\sqrt{n}}\to N(0,1)$

$=\frac{1020-980}{200/\sqrt{100}}=2$

B. Critical value : $Z_{\alpha}=Z_{0.01}=2.33$

The rejection region :

Here , $Z_{stat}=2<Z_{\alpha}=2.33$

Therefore , Do not reject Ho

C. P-value = $P(Z>|Z_{stat}|)=P(Z>2)=0.02275$

D. Here , P-value = 0.02275 > $\alpha=0.01$

Therefore , Do not reject Ho