Question

A certain brand of microwave oven was priced at  stores in Dallas and  stores in San Antonio. The data follow. Use  level of significance and test whether prices for the microwave oven are the same in the two cities.

Dallas	San Antonio
487	478
474	442
461	432
464	457
473	449
457	435
485	443
473	417
409	476
473	425
	432
	423
	479

What is the mean and standard deviation of the normal distribution that can be used for this statistical test?

What is the sum of the ranks for Dallas?

What is the value of the test statistic?

What is the -value for the hypothesis test (to 4 decimals)?

difference between the sample means is (2 decimals)

Answer 1

wilxocon rank sum test ,

Ho: there is no median diference

H1: there is a median difference

sample 1      
sample size ,    n1 =    10
sum of ranks ,    R1 =    150.5
      
sample 2      
sample size ,    n2 =    13
sum of ranks ,   R2 =    125.5
      
R=sum of ranks for smaller sample size =       150.5
      
mean ,µ =    n1(n1+n2+1)/2 =    120
      
std dev,σ =    √(n1*n2*(n1+n2+1)/12) =   16.1245

sum of ranks for Dallas=150.5

Z-stat =    (R - µ)/σ =    1.8915
      
  
P-value =        0.0586
Conclusion:         P-value>α , Do not reject null hypothesis

difference between the sample means is = $20.37