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