Question

Question 1 0 out of 0.05 points The information is for the following 2 questions. Conduct a test and find if the paired variables X are different from the Y at the a 0.05 level bservation 1 Xi 794.5 789.6 793.5 790.1 794.3 791.5 793.2 792.5 794.1 792.4 790.5 797 1. Find s-? Question 2 0 out of 0.05 points The upper boundary of the 95% confidence interval of the difference is Question 3 0 out of 0.05 points The information is for the following 2 questions. Conduct the following test at the α=0.01 level of significance. Assume that the samples were obtained independently using simple random sampling. Test whether the mean of the population 1 is larger 1-40, X1-15.4, S1-1.3; n2-35, x2 14.2, 82-1.2 What is the critical value? Question 4 0 out of 0.05 points What is the P-value?

Answer 1

1)

Ho :   µd=   0
Ha :   µd ╪   0

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
794.5	789.6	4.9	18.49
794.3	793.5	0.8	0.04
791.5	790.1	1.4	0.64
793.2	797	-3.8	19.36
792.5	794.1	-1.6	4.84
792.4	790.5	1.9	1.69

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	4758.4	4754.8	3.6	45.06
mean=	793.0667	792.4667	0.6

sample size ,    n =    6

mean of difference ,    D̅ =   0.6000
      
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    3.002(answer)

std error , SE =    Sd / √n =    1.2256
      
t-statistic =    (D̅ - µd)/SE =    0.4896
      
Degree of freedom, DF=   n - 1 =    5
t-critical value , t* =        2.571
      
p-value =        0.645 [excel function =t.dist.2t(0.4896,5) ]
Conclusion:     p-value>α , Do not reject null hypothesis  

so, X is not different from Y at α=0.05

2)

Degree of freedom, DF=   n - 1 =    5
t-critical value =    t α/2,df =    2.5706
      
std dev of difference , Sd =        3.0020
      
std error , SE =    Sd / √n =    1.2256
margin of error, E =    t*SE =    3.150405
      
mean of difference ,    D̅ =   0.60

confidence interval is       
Interval Upper Limit=   D̅ + E =   3.7504

----------------------------------------------------------------------------------------------------------