Which value can you use for n to show that the first step in a proof by mathematical induction of "For all the positive integers n, 1^2+2^2+...+n^2=n(n+1)(2n+1)/6 " is true? a. n = 3.26
b. n = 1/4
c. n = 1
d. n = -10.1

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).