Listed below are actual high temperature and high temperatures that were forecas

Question

Listed below are actual high temperature and high temperatures that were forecast one day earlier. Construct a 95% confidence interval estimate of the mea difference between actual and forecast temperatures. Interpret the resulting confidence interval. Find the 95% confidence interval. Based on the confidence interval, can the that the difference have a mean of 0 be rejected? A. No, because the confidence interval includes zero. B. No, because the confidence interval does not include zero. C. Yes, because confidence interval includes zero. D. Yes, because the confidence interval does not include zero Is it likely that the forecast accurate? A. Yes, because appears unlikely that the differences have a mean equal to zero. B. No, because it appears likely that the differences have a mean equal to zero. c. No, because it appears unlikely that the difference have a mean equal to zero. D. Yes, because it appears likely that the differences have a mean equal to zero.

Explanation / Answer

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (5-1)*1.58^2+(5-1)*7.26^2/4+4

         = 27.6

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(80-80.8)-0/27.6(1/5+1/5)

       =-0.8/3.32

       =-0.24

Confidence interval:-

(X1-X2)+-ta/2*Sp^2(1/n1+1/n2)

-0.8+-2.306*3.32

LCL=-0.8-7.65592=-8.45592

UCL=-0.8+7.65592=6.85592

(-8.45592,6.85592)

a)

(-8.45592,6.85592)

b)

No, because the confidence interval includes zero.

c)

Yes, because it appears that the difference have a mean equal to zero

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