Stat 4220 Homework
Due February 27
For hypothesis questions use all the steps of a hypothesis

1)  A metal beam is supposed to support 1000 pounds. Assume the standard deviation for failure times is 52 pounds. To test if these beams work you will randomly select 42 beams and measure the weight they can hold before failing. Your average is 990 pounds. Does the data show with α=0.05 that the beams are not working as specified?

2)  The amount of money the Emca company spends on tech support each month is random with a standard deviation of $518. The company wants to know if they are spending $250 on monthly average for tech support. They randomly select 12 months and get a sample average of $1,996. What would their conclusion be using α=0.01?

3)  The amount of time it takes a random computer to load SuperVortex is normally distributed with a standard deviation of 13 minutes. The pop-up window says it takes on average 30 minutes. I randomly selected 7 computers and loaded SuperVortex. My average was 42 minutes. Do I have evidence to disprove what the pop-up window says?

4)  A microwave will naturally exude a random amount of radiation. If the radiation level is 10 mSv or above on average, then it can potentially cause cancer. Researchers are testing if a microwave is safe before sending out on the market

  1. What is the null and alternative hypothesis for their test?
  2. What would be a type I error for this scenario?
  3. What would be a type II error for this scenario?
  4. What would be the definition of power for this scenario?

5)  Ejection seats in the F150 jet push the pilot out of the cockpit with a random amount of force. If the force is too low then the pilot may not be thrown a safe distance from the jet. If the force is too high then the pilot could be injured from the ejection. The government has hired you to test the new ejection seat. If you declare the seat unsafe it will cost the government 10 billion dollars to redraw the specifications and improve the seat. You have been ordered to not use α=0.05. What level of alpha would you pick, and why?

6) The US government is spying on Switzerland. They believe Switzerland is developing a computer virus which will melt all the computers in the US. They are sending in agent 00111 to investigate. He will gather evidence, and if it is strong enough the president will have no choice but to declare war.

a) What is the definition of power in this scenario?
b) What alpha would you suggest and why (explain which consequence you are avoiding)

7) The March 2013 issue of Consumer Reports examined bagless upright vacuums and found an average of 18.4 lbs with a standard deviation of 3.19 lbs. ”Vacuums” Consumer Reports March 2012 pg 44.
Assume that the weights normally distributed. The vacuum company NatureAbhors claims their vacuums are on average lighter than the market average. We sample 5 bagless upright vacuum cleaners from Nature Abhors, and get an average of 18.36. Can we show at the 5% significance level that their average is below the 18.4?

8) The Center for Disease Control reports that from 1999 - 2011 in the United States the number of deaths related to exposure to excessive natural cold has an average of 1301 deaths per year with a standard deviation of 129 deaths. Centers for Disease Control and Prevention. [Number of hypothermia- Related Deaths by Sex]. MMWR 2013;61:[pg 18]. http://www.cdc.gov/mmwr/pdf/wk/mm6151.pdf pg 18

If we sample the next 36 years and get an average of 1260 deaths, will have enough evidence to say the death rate from hypothermia is getting lower?

9) A mechanical engineer builds a machine that makes mirrors consistently with a variance of 0.01 inches in width.The machine is supposed to be calibrated to make a mirror that is 0.05 inches in width, but the QC manager says that it’s not making them thin enough.To find out the mechanical engineer uses it to make 36 mirrors, and the average width from his sample was 0.046.
Use all 7 steps of a hypothesis test to determine who is right.

10) The National Assessment of Educational Progress (NAEP) in science for its fourth grade
students in public schools assessment was updated in 2009 to keep pace with key developments in science. Student performance is presented in terms of average scores on a scale from 0 to 300 with a mean of 150 and a standard deviation of 35. Scores are reported by state. The sample of 104 Wyoming students scored an average of 156. Can you prove that Wyoming students are smarter on average than the rest of the nation?
http://www.nsf.gov/statistics/seind12/pdf/c08.pdf pg. 16

11) An automatic cement mixer dumps in one 50 kg bag of cement mix and then sprays in 22 liters of water. Unfortunately the city water pressure fluctuates, meaning you don’t get exactly 22 liters each time. The good news is that the huge cement mixer repeats this process 120 times to fill the cement truck. If the average for each of the 120 sprays is 22 liters, then the cement will mix well. Assume each time the mixer sprays water is independent (random) of the previous time, and that σ=0.6 liters.

To test if the mixer is working properly an employee of the Sretsbom Company sends an engineer to measure the exact amount of water from 120 sprays. He gets an average of 22.1 liters. Can he say at the 5% significance level the mixer is off on average?