Scott is the owner of a tool and die shop. he has hired you to check his machine’s calibration prior to starting production on a large order. to check this, you set the machine to create 1.5 inch screws and manufacture a random sample of 200 screws. that sample of screws has an average length of 1.476 inches with a standard deviation of 0.203 inches. does this sample provide convincing evidence that the machine is working properly or should it be shut down for repairs?

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) =