Question

Use the following information to answer the next ten exercises: A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds.

13. Identify the following: a. x = ______

b. σ = ______

c. n = ______

14. In words, define the random variable X.

15. In words, define the random variable X.

16. Which distribution should you use for this problem?

17. Construct a 90% confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph, and calculate the error bound.

18. Construct a 95% confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph, and calculate the error bound.

19. In complete sentences, explain why the confidence interval in Exercise 8.18 is larger than in Exercise 8.17.

20. In complete sentences, give an interpretation of what the interval in Exercise 8.18 means.

21. What would happen if 40 heads of lettuce were sampled instead of 20, and the error bound remained the same?

22. What would happen if 40 heads of lettuce were sampled instead of 20, and the confidence level remained the same?

Answer 1

13)

a) sample mean

b) population standard deviation :

c) n=20

14-15) X is the random variable for the weight of each head of lettuce

16) we should be using normal distribution Z score for this test as the population standard deviation is given in the question.

17) The 90% confidence interval for the mean

for 90% confidence

18) For 95% confidence

19) The confidence interval in 18 is larger than17 because of the confidence level of the interval has increased from 90% to 95%.

a narrow confidence interval implies that there is a smaller chance of obtaining an observation within that interval, therefore, our accuracy is higher with 95% confidence interval.

20 It means that we are 95% confident that the population mean of the weight of each head of lettuce lies within the interval