1. (6 points) Your company purchases rubber washers. It is extremely important that the diameter of the hole in the middle of the washer be no different than 0.5 inch. If it is different, the shipment must be returned to the manufacturer. You have just received a shipment of 10,000 washers. There's no way to measure the entire population, so you take a random sample of 35 of them. The sample mean diameter is 0.45 inches, and the standard deviation is calculated to be 0.12 inch. Given this information, is there evidence to suggest that the mean diameter of the entire shipment is something other than what it should be? Use the .05 level of significance to make your decision.
   Using plain language, interpret your statistical decision. Be sure to state whether the shipment should be returned to the sender.
2. (6 points) To be accepted into Stanford's Graduate Business School, a candidate must pass a four hour written entrance exam called the SBSE. Ajax Prep Company offers an expensive study course to prepare a person for this exam. Ajax makes the claim that 80% of the students who finish their course pass the SBSE. Someone who works for a government agency that thinks Ajax's claim is exaggerated and that their true percentage of alumni who pass the SBSE is somewhat lower than 80%. The government worker collects a random sample of 64 students who finished Ajax's course and determines that 43 of them passed the SBSE. Carry out a hypothesis test to see if there is evidence against Ajax's claim. Using the 5% level of statistical significance, is there evidence to suggest that the percentage is lower than Ajax claims?
   Using plain language, interpret your statistical decision.
3. (3 points) A test is carried out to see if the mean diameter of circular crawlspaces in a building is less than 18 inches. The P-value for the test turned out to be 0.4390, which was based on a sample mean of 17.91 inches. Based on this, which of the following can you conclude?

1. The mean diameter of all of the crawlspaces is definitely not 18 inches
2. There is evidence to suggest that the mean diameter is something other than 18 inches.
3. All we can say is that the mean diameter of all of the crawlspaces is less than 18 inches.
4. There is no evidence to suggest the mean diameter of all of the crawlspaces less than 18 inches.
5. I still don't know what a P-value does exactly

1. (6 points) Researchers from the Journal of Personality and Social Psychology conducted a study to see if men who were professors or medical doctors had different testosterone levels than men in the general population. Medically speaking, it is estimated that the average testosterone level (measured in nanograms per deciliter) for the general adult male population is 10.70. The average testosterone level for the 26 doctors and professors in the study was 11.15, and the standard deviation of the levels was 2.59. Does this sample outcome provide sufficient evidence that the average testosterone level for all male doctors and professors is different than that of the general adult male population? Make your decision using the .05 level of significance.
   Using plain language, interpret your statistical decision.
2. (6 points) A researcher was interested in estimating whether younger college students got enough sleep. He asked 28 randomly selected college students how many hours of sleep they got on a "typical" evening. The average amount of sleep for those sampled was 6.7223 hours per night, and the standard deviation for the sleep times was 1.6223 hours per night. Given this information, test to see if there is significant evidence to suggest that the true mean amount of nightly sleep for all college students is less than 7 hours per night. Use the 0.05 level of significance to make your statistical decision.
   Using plain language, interpret your statistical decision.
   6. (3 points) An auto manufacturer needs to test to see if the percentage of its airbags that are defective is greater than 2%. If it is found to be higher than 2%, production must be halted until the problem is corrected. Which type of error would be more detrimental for the consumers of this company's automobiles (in terms of safety)?
   1. Type I b. Type II c. Neither, as long as they do all of their calculations correctly.
      d. Neither would be bad for the consumer, but both would be bad for the manufacturer.

7. (3points) In testing the hypothesis

The p-value is found to be .0738, and the sample mean is 105. Which of the following statements is true?

1. The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is .0738.
2. The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is .0738
3. The probability that the population mean is larger than 100 is .0738
4. The probability of observing a sample mean at least as large as 100 from a population whose mean is 105 is .0738.
5. None of the above statements is correct

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