1. conducted research of a random sample of 49 manufactured products. The average weight of the sample is 3.5kg. Assume that the standard deviation of all manufactured products is 0.75kg. Find a 90% confidence interval for the population mean average work.

a. (1 points) n =

b. (1 points) x-bar =

c. (1 points) sigma =

d. (1 points) alpha =

e. (2 points) z =

f. (4 points) Calculate the confidence interval CI for mu. Show your calculation below:

CI =

2. Pringles are supposed to contain 5.2 oz of potato chips. However, there are some complaints coming from customers. They claim that actual weight is less than 5.2 oz. An inspector, comes to the factory and takes a sample of 25 products. The average weight of the sample is 4.85 oz. Assume that the standard deviation of the distribution is 0.8 oz. Test the hypotheses at alpha = 0.05 level. To answer the question, follow the steps below:

a. (2 points) State Ho: State Ha: b. (1 points) x-bar = c. (1 points) mu = d. (1 points) sigma = e. (1 points) n = f. (3 points) Calculate the z-score. Show your calculation below: z = g. (1 point) p - value = h. (2 points) Do you reject Ho for Ha? Why? i. (1 points) State your conclusion in plain English:

3. Assume that the standard deviation of household income in the Land is 6000 dollars.

You take a sample of 250 households and test the following hypothesis at alpha =0.01. Ho: mu = 50000 dollars Ha: mu >= 50000 dollars

To answer the question, follow the steps below:

a. (1 points) mu =

b. (1 points) n =

c. (1 points) sigma =

d. (1 points) alpha =

e. (8 points) What is the lowest income (x-bar) that will allow you to reject Ho?

Show your calculation below: z = x-bar = f. (8 points)

What is the power of this test if mu actually is 51000 dollars? Show your calculation below: