For the given​ data, (a) find the test​ statistic, (b) find the standardized test​ statistic, (c) decide whether the standardized test statistic is in the rejection​ region, and​ (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent. Claim: μ1<μ2​, α=0.01. Sample​ statistics: x1=1220, n1=35, x2=1190, and n2=65. Population​ parameters: σ1=65 and σ2=105. Part 1 ​(a) The test statistic for μ1−μ2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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For the given​ data, (a) find the test​ statistic, (b) find the standardized test​ statistic, (c) decide whether the standardized test statistic is in the rejection​ region, and​ (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent.
Claim: μ1<μ2​, α=0.01.
Sample​ statistics: x1=1220, n1=35, x2=1190, and n2=65. Population​ parameters: σ1=65 and σ2=105.
Part 1
​(a) The test statistic for μ1−μ2 is _____
 
b) The standardized test statistic for
μ1−μ2 is _______
​(Round to two decimal places as​ needed.)
 
Part 3
​(c) Is the standardized test statistic in the rejection​ region?
 
Part 4
 
 
​(d) Should you reject or fail to reject the null​ hypothesis?
 
H0​: μ1≥μ2​; Ha​: μ1<μ2. (Fail to reject/Reject) H0. At the​ % significance​ level, there is (not enough/ enough) evidence to support the claim.
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