Hypothesis test

The production line that packages boxes of raisins at a snack food manufacturer will be considered operating properly if the average weight of the boxes of raisins is 1.5 ounces with a standard deviation of 0.1 ounces. A random sample of 16 boxes showed an average weight of 1.45 ounces.

1. How can I find the null and alternative hypothesis to determine if the production line is operating properly.

2. What additional assumption is needed before we can perform a test to determine whether the production line is operating properly?

3. State the value of the correct rejection region for α = 0.05

4. State the correct rejection region for α = 0.01

5. What should be the correct decision and conclusion when testing to determine if the production line is operating properly by allowing a 10% probability of committing a Type 1 error?
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An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments based upon the size of the apartment as defined by square footage. A sample of 25 apartments in a particular residential neighborhood was selected and the information gathered revealed the following:

Apartment Rent ($) Size (sf) Apartment Rent ($) Size (sf)
1 950 850 14 1,800 1369
2 1,600 1450 15 1,400 1175
3 1,200 1085 16 1,450 1225
4 1,500 1232 17 1,100 1245
5 950 718 18 1,700 1259
6 1,700 1485 19 1,200 1150
7 1,650 1136 20 1,150 896
8 935 726 21 1,600 1361
9 875 700 22 1,650 1040
10 1,150 956 23 1,200 755
11 1,400 1100 24 800 1000
12 1,650 1285 25 1,750 1200
13 2,300 1985

1. Use the least squares method to find the regression coefficients b0 and b1.

2. State the simple linear regression equation

3. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet with a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. What would you recommend to them? Why?