Question

A coffee company sells bags of coffee beans with an advertised weight of 454 grams. A random sample of 20 bags of coffee beans has an average weight of 457 grams. Weights of coffee beans per bag are known to follow a normal distribution with standard deviation 7 grams. (a) Construct a 95% confidence interval for the true mean weight of 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 to determine if there is evidence that the true mean weight of all bags of coffee beans differs from 454 grams. You will be marked on your calculation of the appropriate test statistic, P-value and a carefully worded conclusion. (d) Provide an interpretation of the P-value in (c). (1 mark) (e) Could the confidence interval in (a) have been used to conduct the test in (c)? Explain why or why not. If it could have been used, what would your conclusion be and why? (1 mark)

Answer 1