## Question

###### A paint manufacturing company claims that the mean drying time for its paints is not longer than 45 minutes. A random sample of 20 gallons of paints selected from the production line of this company showed that the mean drying time for this sample is $49.50$ minutes with a standard deviation of 3 minutes. Assume that the drying times for these paints have a normal distribution.a. Using the $1 %$ significance level, would you conclude that the company's claim is true?b. What is the Type I er

A paint manufacturing company claims that the mean drying time for its paints is not longer than 45 minutes. A random sample of 20 gallons of paints selected from the production line of this company showed that the mean drying time for this sample is $49.50$ minutes with a standard deviation of 3 minutes. Assume that the drying times for these paints have a normal distribution. a. Using the $1 %$ significance level, would you conclude that the company's claim is true? b. What is the Type I error in this exercise? Explain in words. What is the probability of making such an error?

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