Question 2 Suppose we have a new method of blowing crystal glass We seek to demonstrate that our new method has a lower rate of imperfections than our current method which has an imperfection rate of 0 240 We have set our significance level to 0 005 Our hypothesis pair is OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 OHO p 0 240 HA p 0 240 Considering our significance level and using the standard normal model our Critical Region for our test statistic z is closest to less than or equal to 3 09023 Oless than or equal to 2 05375 less than or equal to 2 32635 Oless than or equal to 2 57583 Oless than or equal to 1 64485 Suppose employing our new method through a mechanism that mimics randomization we create 903 crystal glassworks and our observed sample statistic is p hat 0 24031 Using the standard normal model our observed test statistic z is closest to 00 021812 O 5 666164 O 2 081979 02 125603 O 7 069161 Our decision is Owe fail to reject the null hypothesis and do not conclude our new method out performs our current method in terms of rate of imperfections We reject the null hypothesis and conclude our new method out performs our current method in terms of rate of imperfections