Provided below are summary statistics for independent simple random samples from two populations. Use the pooled​ t-test and the pooled​ t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.   x1=20​, s1=4​, n1=12​, x2=18​, s2=5​, n2=13   a.​ Right-tailed test, α=0.05 b. 90​% confidence interval   a. What are the correct hypotheses for a​ right-tailed test?   A. H0​: μ1=μ2 Ha​: μ1≠μ2   B. H0​: μ1<μ2 Ha​: μ1=μ2

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Provided below are summary statistics for independent simple random samples from two populations. Use the pooled​ t-test and the pooled​ t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
 
x1=20​,
s1=4​,
n1=12​,
x2=18​,
s2=5​,
n2=13
 
a.​ Right-tailed test, α=0.05
b. 90​% confidence interval
 
a. What are the correct hypotheses for a​ right-tailed test?
 
A. H0​: μ1=μ2 Ha​: μ1≠μ2
 
B. H0​: μ1<μ2 Ha​: μ1=μ2
 
C. H0​: μ1=μ2 Ha​: μ1<μ2
 
D. H0​: μ1≠μ2 Ha​: μ1=μ2
 
E. H0​: μ1>μ2 Ha​: μ1=μ2
 
F. H0​: μ1=μ2 Ha​: μ1>μ2
 
Compute the test statistic.
 
t=______________
​(Round to three decimal places as​ needed.)
 
Determine the critical value.
 
tα=____________
​(Round to three decimal places as​ needed.)
 
What is the conclusion of the hypothesis​ test?
 
Since the test statistic___________(is or is not) in the rejection​ region,
__________ (reject or do not reject) H0.
 
b. The 90​% confidence interval is from _______ to ________.
​(Round to three decimal places as​ needed.)
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