Find the following critical t-values round to 3 decimal places . a) critical t value for the 98% confidence interval with n = 25 , t = b) critical value for t tests for n = 15, 5% significance level, right-tailed. t = c) critical value for t tests for n = 20, two-tailed with 10% significance level. t = d) critical value for t tests for n = 50, left-tailed , with 1% significance level. t =Breaking Strength of Rope: A rope manufacturer, after conducting a large number of tests over a long period of time, has found that the rope has a mean breaking strength of 300 pounds and a population standard deviation of 24 pounds (o = 24 /bs). It is believed that by using a recently developed high-speed process, the mean breaking strength has been decreased. Forty-five tests resulted in a sample mean of 294 pounds. Test the claim at 5% significance level. Perform a hypothesis test using the 5-step process: a) State Ho and H1 in symbols and in words. Identify which hypothesis is the claim and determine the type of test (right-tail, left-tail, two tail). b) Determine the critical value and label it (for example, z = 1.96 ort = -2.421, etc). c) Compute the test value. If you are using the p-value method, then include the p-value of the test. d) Make the decision to Reject Ho or Do not reject Ho. e) State your complete conclusion in the context of the claim.Handing Machines, Coffee: A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 10 ounces. Nine cups of coffee from this machine show that the average content to he 13 ounces with a standard deviation of {1.5 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is more than II" ounces? Use a 5% level of signicance. Question: Perform a hypothesis test using the 5-step process: a} State Ho and H1 in svmbols and in words. Identify which hvpothesis is the claim and determine the type of test [righttail. lefttoil, two tail]. b} Determine the critical value and label it -- for example. 2 = 1.55:5 ort = 4.21, etc}. cl Compute the test value. If 1vou are using the p-value method, then compute the test value and p- value of the test. d} Make the decision to Reject Ho or Do not reject Ho. e} State your complete conclusion in the context of the claim