A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of this primary supplier. The data collected is presented in the table below with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Material	Primary Supplier	Secondary Supplier	Difference
1	$55	$45	$10
2	$48	$47	$1
3	$31	$32	-$1
4	$83	$77	$6
5	$37	$37	$0
6	$55	$54	$1
Sum	$309	$292	$17
Sum of Squares	$17573	$15472	$139

a ) The hypotheses that the buyer should test are a null hypothesis that ___________ versus an alternative hypothesis that ___________.

b) The test to perform is a

i)Pooled-variance t test for differences between two means.

ii) Separate-variance t test for differences between two means.

iii) Z test for the difference between two proportions.

iv) Paired t-test for the mean difference.

c) The decision rule is to reject the null hypothesis if ________.

d) The calculated value of the test statistic is ______. 1.628.

e) The p-value of the test statistic is _______.

f) True or False. The null hypothesis should be rejected.

Please include the formulas and the steps involved in arriving at the answers with the Decsions associated for the above problem ( would like to arrive at the answers with out using EXCEL or Minitab) .