Answer to Question #214535 in Statistics and Probability for Madimetja

Question

A consumer organisation wants to obtain information about , the mean number of drawing pins in the boxes of a certain brand which, according to the label, should contain 100 pins. In nine randomly chosen boxes this organisation finds the following numbers of drawing pins:

 90       94       88       92       90       86       94       90       86

 

  (a) (i) Test whether  < 100. Take as level of significance  a= 0:05.  

(ii) Which assumption do you need?

(b) If the true value of u is 101, what type of error did you make in part (a)?

(c) (i) Determine a 90% confidence interval for u  

(ii) Is it likely that  u= 101?