Question

Use the given sample statistics to test the claim about the difference between two population means

mu 1μ1 and mu μ2 at the given level of significance alphaα=0.01.

Claim: mu 1μ1greater than>mu 2μ2,

Statistics: x overbar 1=5.2, s1=0.30, n1=48 and x overbar 2=5.6, s2=0.7 n2=37

Choose the correct null and alternative hypotheses below.

A. Upper H 0: mu 1greater thanmu 2 (Claim) Upper H Subscript a: mu 1less than or equalsmu 2

B. Upper H 0: mu 1not equalsmu 2 Upper H Subscript a: mu 1greater thanmu 2 (Claim)

C. Upper H 0: mu 1equalsmu 2 Upper H Subscript a: mu 1greater thanmu 2 (Claim)

D. Upper H 0: mu 1less than or equalsmu 2 Upper H Subscript a: mu 1greater thanmu 2 (Claim)

Determine the critical value(s).

z0=_______(Round to two decimal places as needed. Use a comma to separate answers as needed.)

Determine the rejection region. Select the correct choice below, and, if necessary, fill in any answer boxes to complete your choice. (Round to two decimal places as needed.)

A. zless than ______

B. zgreater than _______

C. zless than _____ and zgreater than _______

Calculate the standardized test statistic.

z=______(Round to two decimal places as needed.)

Choose the correct answer below.

A. Reject Upper H 0. At the 1% significance level, there is enough evidence to support the claim.

B. Fail to reject Upper H 0. At the 1% significance level, there is enough evidence to support the claim.

C. Reject Upper H 0. At the 1% significance level, there is not enough evidence to support the claim.

D. Fail to reject Upper H 0. At the 1% significance level, there is not enough evidence to support the claim.

Answer #1

(A)Claim is that mu1 is greater than mu2

so, we can write

Ho: mu1 = mu2

H1: mu1 > mu2

option C

(B) z critical = NORMSINV(alpha)

where alpha = 0.01

z critical = NORMSINV(0.01) = 2.33 (positive value for right tailed hypothesis)

rejection region is **z greater than 2.33**

(C) Using TI 84 calculator

press stat then tests then 2-sampZTest

xbar1=5.2, s1=0.30, n1=48

xbar2=5.6, s2=0.7 n2=37

mu1>mu2

press **ENTER**

test statistic = -3.25

test statistic is not greater than z critical value, so we failed to reject the null hypothesis

option D

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