(Solved): 6) A consumer protection agency wants to establish the mean drying time of its paints. It is assume ...

6) A consumer protection agency wants to establish the mean drying time of its paints. It is assumed from past experience the standard deviation of such drying time is \( \sigma=2.4 \) minutes. The manufacturer tests the null hypothesis \( H_{0}: \mu=20 \) minutes vs. the alternative hypothesis \( H_{1}: \mu>20 \) minutes. The manufacturer used a sample of 36 one-gallon cans of paint and decided to reject his claim if \( \bar{X}>20.50 \). Find the probability of Type I error. a) \( 0.0778 \) b) \( 0.1056 \) c) \( 0.0951 \) d) \( \mathbf{0 . 1 0 7 5} \) 17) If a random sample of size \( n \) is selected from an infinite population having mean 96 and standard deviation 12. How large must \( n \) be in order that Chebyshev's Theorem asserts that \( P(93 \leq \bar{X} \leq 99) \geq 0.36 \) ? a) 25 b) 48 c) 64 d) 76