A coffee company sells bags of coffee beans with an advertisedweight of 454 grams. A random sample of 20 bags of coffee beans hasan average weight of 457 grams. Weights of coffee beans per bag areknown to follow a normal distribution with standard deviation 5grams.
(a) Construct a 95% confidence interval for the true mean weightof all bags of coffee beans. (Instead of typing ±, simply type +-.)(1 mark)
(b) Provide an interpretation of the confidence interval in (a).(1 mark)
(c) Conduct a hypothesis test at the 5% level of significance todetermine if there is evidence that the true mean weight of allbags of coffee beans differs from 454 grams. You will be marked onyour calculation of the appropriate test statistic, P-value and acarefully worded conclusion.
(d) Provide an interpretation of the P-value in (c). (1mark)
(e) Could the confidence interval in (a) have been used toconduct the test in (c)? Explain why or why not. If it could havebeen used, what would your conclusion be and why? (1 mark)
