Hello, I have two homework questions that I have completed. I would like to know if I did them correctly.

1. ABC Inc. carries inventory of 2000 items. The population standard deviation for the cost of the inventory is = 144. A consultant recommends that the company takes a sample of 160 items from its inventory to estimate the average cost per item. Please answer the following questions: a. What is the standard error of the sampling distribution of ? b. What is the probability that the sample mean will be within 25 of the population mean ?

Answer:

Standard error = 144 / (160^0.5) = 11.38

b + 25 = + (25/11.38) standard error = 2.2 standard error

P(z < -2.2) = 0.014

P(z > 2.2) = 0.986

P(-2.2 < z < 2.2) = 0.972

2. The United States ranks ninth in the world in per capita chocolate consumption; Forbes reports that the average American eats 9.5 pounds of chocolate annually. Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of the Hershey Company's corporate headquarters. A sample of 36 individuals from the Hershey area showed a sample mean annual consumption of 10.15 pounds and a sample standard deviation of s = 1.8 pounds. Using = .05, do the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the United States?

Answer:

H0: mu = 9.5

Ha: mu > 9.5

t = (10.15 - 9.5) / (1.8 / (36^0.5)) = 2.167

Probability = 1 - 0.981 = 0.019

Since it is less than 0.05, the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the United States