Defn: A continuous r.v. X is said to have an F-distribution with m (numerator) and n (denominator) degrees of freedom (d.f.) if, and only if, the PDF of X is given by Notation: Mean : Variance: r(-) 士(帶)(③) w X-F(m.) E(X) = n n-2 m * Var(X) = DNE n>2 x(%)-1 (1+x)(0)(x), m.nez". 2n² (m+n-2) m(n-2)(n-4) n>4 Theorem: Let U-X) and V-X), with U and V independent. Then, MGF : Note: Prove F-distribution. Note: Use the proof of t-distribution as reference. X=-Fm %

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?   67 82 38 66 43 22 63 64 68 47 67 73 91 90     Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?   A. H0​: μ=60 seconds H1​: μ≠60 seconds B. H0​: μ=60 seconds H1​: μ<60 seconds   C. H0​: μ=60 seconds H1​: μ>60 seconds   D. H0​: μ≠60 seconds H1​: μ=60 seconds   Determine the test statistic.   ​(Round to two decimal places as​ needed.)   Determine the​ P-value.   ​(Round to three decimal places as​ needed.)

12n-10=50

I need help answering #7

3x + 5y = 32.75 4x + 4y = 29