Question

A certain brand of microwave oven was priced at 10 stores in Dallas and 13 stores in San Antonio. The data follow.

Dallas	San Antonio
443	461
488	454
403	433
483	478
438	473
448	443
436	428
421	435
431	411
403	420
	423
	458
	431

Use a 0.05 level of significance and test whether prices for the microwave oven are the same in the two cities.

State the null and alternative hypotheses.

H₀: Median price for Dallas − Median price for San Antonio < 0
H_a: Median price for Dallas − Median price for San Antonio = 0H₀: The two populations of microwave prices are identical.
H_a: The two populations of microwave prices are not identical.    H₀: Median price for Dallas − Median price for San Antonio ≤ 0
H_a: Median price for Dallas − Median price for San Antonio > 0H₀: Median price for Dallas − Median price for San Antonio ≥ 0
H_a: Median price for Dallas − Median price for San Antonio < 0H₀: The two populations of microwave prices are not identical.
H_a: The two populations of microwave prices are identical.

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the prices for the microwave oven in the two cities.Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the prices for the microwave oven in the two cities.    Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the prices for the microwave oven in the two cities.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the prices for the microwave oven in the two cities.

Answer 1

H₀: The two populations of microwave prices are identical.
H_a: The two populations of microwave prices are not identical.   

Dallas	San Antonio	Dallas Values	Dallas Ranks	San Ant.Values	San Ant. Ranks
443	461	403	1.5	411	3
488	454	403	1.5	420	4
403	433	421	5	423	6
483	478	431	8.5	428	7
438	473	436	12	431	8.5
448	443	438	13	433	10
436	428	443	14.5	435	11
421	435	448	16	443	14.5
431	411	483	22	454	17
403	420	488	23	458	18
	423			461	19
	458			473	20
	431			478	21

Result Details

Dallas
Sum of ranks: 117
Mean of ranks: 11.7
The expected sum of ranks: 120
The expected mean of ranks: 12
U-value: 68
Expected U-value: 65

San Antonio
Sum of ranks: 159
Mean of ranks: 12.23
The expected sum of ranks: 156
The expected mean of ranks: 12
U-value: 62
Expected U-value: 65

Dallas & San Antonio Combined
Sum of ranks: 276
Mean of ranks: 12
Standard Deviation: 16.1245

Result 1 - U-value

The U-value is 62. The critical value of U at p < .05 is 33. Therefore, the result is not significant at p < .05.

Result 2 - Z-ratio

The Z-Score is 0.15504. The p-value is .87288. The result is not significant at p < .05.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the prices for the microwave oven in the two cities.