A student wants to determine if there is a difference in the pricing between two stores for health and beauty supplies. She recorded prices from both stores for each of 10 different products. Assuming that the conditions for conducting the test are satisfied, determine if there is a price difference between the two stores. alpha = 0.05 level of significance.

Store 1 Store 2
Product A 5.92 5.85
Product B 7.53 7.93
Product C 3.75 3.98
Product D 1.81 1.71
Product E 1.71 1.96
Product F 2.86 2.58
Product G 4.79 4.74
Product H 3.18 3.69
Product I 3.02 2.87
Product J 3.77 3.68

Required:
a. Use technology to calculate the P-value.
b. Draw a conclusion based on the hypothesis test.

The P-value  is 0.04542 which is less than 0.05

Since the calculated value of t does not fall in the critical region so we accept H0 that there is no price difference between the two stores.

Step-by-step explanation:

          Store 1        Store 2        Difference (Store 2-1)        d²

Product A 5.92       5.85             -0.07                                 0.0049

Product B 7.53         7.93               0.4                                    0.16

Product C 3.75             3.98           0.23                             0.0529

Product D 1.81              1.71             -0.1                               0.01

Product E 1.71                1.96           0.25                         0.0625

Product F 2.86               2.58          - 0.28                    0 .0784

Product G 4.79                4.74           -0.05                     0.0025

Product H 3.18                3.69             0.51                     0.2601

Product I 3.02                2.87               - 0.15                         0.0225

Product J 3.77                  3.68                -0.09                      0.0081

∑                                                                 0.65                      0.6619  

1. The degrees of freedom = n-1= 10-1= 9

2. The significance level is 0.05

3.The test statistic is

t= d`/sd/√n

4. The critical region is ║t║≥ t (0.025,9) = 2.262

The null and alternate hypotheses is

H0 : ud= 0 against Ha: ud≠ 0 (two tailed test)

5. Calculations

d`= ∑di/n= 0.65/10= 0.065

Sd²= ∑(di-d`)²/n-1 = 1/n-1 [∑di²- (∑di)²n]

Sd²= 1/9[0.6619-(0.65)²/10] = [0.6619-0.4225/9]= 0.0266

Sd= 0.163

Therefore

t= d`/ sd/√n

t= 0.065/ 0.163/√10

t= 0.3987/3.1622=0.1261

6. Conclusion

Since the calculated value of t does not fall in the critical region so we accept H0 that there is no price difference between the two stores.

Now the P- value:

The P-value is the rejection region. In this test it is on both sides and would add up to be (2.262 + 2.262)/100= 4.542/100

The P-value  is 0.04542 which is less than 0.05