In set of prime numbers P 2, find the change-of-coordinates matrix from the basis Upper B equals StartSet 1 minus 3 t plus t squared comma 2 minus 5 t plus 3 t squared comma 3 t plus 4 t squared EndSet to the standard basis Upper C equals StartSet 1 comma t comma t squared EndSet. Then find the B-coordinate vector for negative 2 plus 7 t.

Atest of sobriety involves measuring the subject's motor skills. a sample of 31 randomly selected sober subjects take the test and produce a mean score of 64.4 with a standard deviation of 2. a claim is made that the true mean score for all sober subjects is equal to 65. for each part below, enter only a numeric value in the answer box. for example, do not type "z =" or "t =" before your answers. round each of your answers to 3 places after the decimal point. (a) calculate the value of the test statistic used in this test. test statistic's value = (b) use your calculator to find the p-value of this test. p-value = (c) use your calculator to find the critical value(s) used to test this claim at the 0.2 significance level. if there are two critical values, then list them both with a comma between them. critical value(s) =