Recently a sample of 36 pieces of thread showed a mean breaking strength of 8.93 oz. Can one conclude at a significance level of (a) 0.05, (b) 0.01 that the thread has become inferior?

Complete Question

It has been found from experience that the mean breaking strength of a particular brand of thread is 9.72 oz with a standard deviation of 1.4 oz. Recently a sample of 36 pieces of thread showed a mean breaking strength of 8.93 oz. Can one conclude at a significance level of (a) 0.05, (b) 0.01 that the thread has become inferior?

At both and    the conclusion is that the thread has become inferior

Step-by-step explanation:

From the question we are told that

      The population  mean is  

      The standard deviation is  

       The sample size  is  n =  36

        The sample mean is  

The  null hypothesis is  

The  alternative hypothesis is  

     Generally the test statistics is mathematically represented as

=>        

=>      

So  

    The  p-value obtained from the z- table is  

So at  

So we reject the null hypothesis,hence we conclude that the thread has become inferior

  So at  

So we reject the null hypothesis,hence we conclude that the thread has become inferior

It is pi over 6:

We first solve this by determining how many times it goes around the circle. When you turn 25pi/6 into a mixed number you get 4pi + 1pi/6. Since it takes 2pi to get around the circle once, you go around the circle twice with 4pi. This leaves with 1pi/6 left at the starting point. The answer is pi/6. 13pi/6 also has the same terminal angle but it is not in range of answers (they are asking for 0-2pi)