The length of a construction part manufactured by a supplier follows a normal distribution with an unknown σ. The design length is 33.00 centimeters. Seven parts were randomly selected from the warehouse and measured. The actual lengths in centimeters were as follows: Questions: 10 αv 0.950 0.960 0.975 0.980 0.995 1 Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 38.39 31.82 36.67 38.31 32.08 34.36 40.50 (a)[6] At α = 0.04, test to see if a typical manufactured part would conform to the design length. Make sure to define the hypotheses first, make a sketch of the test, and then carry out the test. (b)[4] Sketch and find the p‐value. Would you reject the null if α = 0.07? Explain with a sketch. Hint: Use 5 decimals. Refer to some Excel lookups:

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Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12