Question

A professor in the School of Business wants to investigate the prices of new textbooks in the campus bookstore and the Internet. The professor randomly chooses the required texts for 12 business school courses and compares the prices in the two stores. The results are as follows:

Book	Campus Store	Internet Price
1	$55.00	$50.95
2	47.50	45.75
3	50.50	50.95
4	38.95	38.50
5	58.70	56.25
6	49.90	45.95
7	39.95	40.25
8	41.50	39.95
9	42.25	43.00
10	44.95	42.25
11	45.95	44.00
12	56.95	55.60

a)At the .01 level of significance, is there any evidence of a difference in the average price of business textbooks between the campus store and the Internet? Use Excel and the classical method.

1. Hyps: H₀:  

2. H₁:

3. Test(s):
4. Decision rule:

5. analysis

6. conclusion:(1)

   (2)

   (3)

   (4)

   b) What assumptions are necessary to perform this test?

   c)Find the p-value in (a)? Using the p-value, Is there any evidence of a difference in the average price of business textbooks between the campus store and the Internet? Use Excel and the p-value method and alpha = 1%.

   1. Hyps: H₀: 2. H₁:

7. Test(s):

8. analysis

9. p- value

10. conclusion:(1)

    (2)

    (3)

    (4)

Answer 1

SOLUTION 1a: NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

LEVEL OF SIGNIFICANCE =0.01

test statistic t= 3.365

Rejection Region

Based on the information provided, the significance level is α=0.01, and the degrees of freedom are df=11.Hence, it is found that the critical value for this two-tailed test is tc​=3.106, for α=0.01 and df=11.

The rejection region for this two-tailed test is R={t:∣t∣>3.106}.Since it is observed that ∣t∣=3.365>tc​=3.106, it is then concluded that the null hypothesis is rejected.

Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ for campus is different than μ2 internet price​, at the 0.01 significance level.

Using the P-value approach: The p-value is p=0.0063, and since p=0.0063<0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ for campus is different than μ2 internet price​, at the 0.01 significance level.

Since P value SMALLER THAN THE LEVEL OF SIGNIFICANCE THEREFORE SIGNIFICANT.