7. The drying time of a type of paint under specified test conditions is known to be normally distributed with a mean value of 75 min and a standard deviation of 9 min. Chemists have proposed a new additive desinged to decrease average drying time. It is believed that drying times with this additive will remain normally distributed with o = 9. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average dry- ing time before such a conclusion is adopted. Let u denote the true average drying time when the additive is used. The appropriate hypotheses are Ho : µ = 75 versus Ha : u < 75. Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesis if the sample mean from this sample is less than 71.5 minutes. (a) Find the value of a, the probability of a type I error, for this test. (b) of μ = 70. Find the value of B(70), the probability of a type II error when the true value

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.