Each of following summaries of hypothesis tests contain one or more errors (possibly including calculation errors) or issues that invalidate the process or the conclusion. Identify and describe these. [2+2+2+2 =8 marks] a) Scenario: Mean hourly production was historically 101.1 kg per hour with a standard deviation of 23.4 kg. After a process change a random sample of 87 hours reveals a sample mean of 107.4 kg per hour. Has average hourly production changed? [2 marks] Ho: H = 101.1 vs HA: # # 101.1 X = 107.4, 6=23.4, n=87, a=0.05, N very large and unknown Ztest = 2.511, Zchit = +/-1.96 Decision: retain Ho Conclusion: Average production hasn't changed. b) Scenario: 8 throws of a coin produces only 2 heads. Is the coin biased in favour of tails? (p=proportion that are heads) [2 marks] Ho:p = 0.5 (alternatively expressed as Ho: p 2 0.5 ) vs HA:p