6.1 1 a) and b) let x be a string of length n, and let y be a string of length n − k, for 1 ≤ k < n. we wish to line up the symbols in x with the symbols in y by adding k blanks to y. a) suppose that we decide to add the k blanks in one continuous block. how many ways are there to do this? b) suppose that we add two separate blocks of blanks, one of size i and one of size k − i, for 1 ≤ i < k. how many ways are there to do this?

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) =