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

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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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