Acompany that manufactures brackets for an automaker regularly selects brackets from the production line and performs a torque test. the goal is for mean torque to equal 125 let x equal the torque and assume that x is n(mu, sigma^2). we shall use a sample of size n = 15 to test h0: mu = 125 against a two-sided alternative hypothesis. (a) give the test statistic and a critical region with significance level a = 0.05. sketch a figure illustrating the critical region.
we want to verify that;
we take only the expression on the left hand side and work to get the expression on the right hand side.
we cancel the common factors to get;
we now use the pythagorean identity;
we make the subject to obtain;
the basic trigonometric identity we used is
an event with a probability of 0 is impossible.
an event with a probability of 1 is certain.
probability is typically expressed in terms of a fraction between 0 and 1 where the denominator is the total number of outcomes and the numerator is the number of desired outcomes. since probability is expressed as a fraction, if the probability is 0, that means it is impossible, or there is no chance that the event can happen. however, if the probability is 1, that means that the event is certain to happen and the odds are completely in your favor that the event will happen.
65/500, 5/8, 2/3, 7/10
2/3= 0.66 (repeating)