A customer service representative was interested in comparin

A customer service representative was interested in comparing the average time (in minutes) customers are placed on hold when calling Southern California Edison and Southern California Gas companies. The representative obtained two independent random samples and calculated the following summary information: So Cal Edison Southern Cal Edison Southern Cal Gas Sample Size 9 12 Sample Mean 3.2 min 2.8 min Sample Standard deviation 0.5 min 0.7 min Assume the distributions of time a customer is on hold are approximately normal. Using the null and alternate hypothesis: H0:mu1-mu2=0 vs. Ha:mu1-mu2 not equal 0 The test statistic was computed to be -1.455 Assuming alpha = 0.10, set up the appropriate rejection region for the hypothesis test. A. Reject H0 if |t| > t(alpha =0.1, df=20) B. Reject H0 if |t| > t(alpha =0.05, df=19) C. Reject H0 if |t| > t(alpha =0.05, df=20) D. Reject H0 if |t| > t(alpha =0.1, df=19)

Solution

Set Up Hypothesis
Null, Ho: u1 = u2
Alternative, H1: u1 != u2
Test Statistic
X (Mean)=3.2; Standard Deviation (s.d1)=0.5
Number(n1)=9
Y(Mean)=2.8; Standard Deviation(s.d2)=0.7
Number(n2)=12
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (8*0.25 + 11*0.49) / (21- 2 )
S^2 = 0.3889
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=3.2-2.8/Sqrt((0.3889( 1 /9+ 1/12 ))
to=0.4/0.275
to=1.4546
| to | =1.4546
Critical Value
The Value of |t | with (n1+n2-2) i.e 19 d.f is 1.729

[ANSWER] D. Reject H0 if |t| > t(alpha =0.1, df=19)