Can you show the work by hand, please?

1. Explain the difference between (a) and (b) below:

(a) H₀: m = 100 (b) H₀: m = 100

H₁: m 100 H₁: m > 100

2. SAT tests are typically taken by the students who plan to attend college, so not all high school students take them. You suspect that the average SAT score for those students is higher than if ALL high school students took the SAT, so you design a study to test your hypothesis. You randomly select 500 high school seniors and administer the SAT. You obtain a sample mean of 461 (sample standard deviation = 95).

Assume that the SAT test is standardized with a mean of 475 and a standard deviation of 100.

(a) What is the appropriate hypothesis test? Why?

(b) Perform the test and show ALL work (including formulas, H₀ and H₁, etc.) and all steps for the hypothesis test.

(c) What is your decision regarding your hypothesis? What conclusions can you make from your study?

3. You are the manager at a small company that bottles beer and other drinks. A manufacturer says that they have a new bottling machine that cap bottle 100 bottles every 5 minutes. He offers to let you try it out. You test the new machine for four hours and then you randomly select 10 5-minutes periods and record how many bottles were capped during each 5-minute period. Your results are shown below. Do you decide to buy the new machine?

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