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For problems involving actual hypothesis testing of data, the following steps are required:
a) State the appropriate hypotheses
b) Report the critical value.
c) Report the test statistic
d) State your decision regarding H0.
e) Report the p-value.
1. Use the criminal justice system in the US to provide an example of a Type I error.
2. Use the criminal justice system in the US to provide an example of a Type II error.
3. Mike Trout of the Anaheim Angels thinks his batting average exceeds 0.320. What are the appropriate hypotheses associated with this claim?
4. Motorola invented the concept of six-sigma – claiming production of less than 3.4 defects per million units produced. What are the appropriate hypotheses associated with this claim?
5. LeBron James claims that when Cleveland plays Chicago in basketball, Cleveland beats them by an average of six points. What are the appropriate hypotheses associated with this claim?
6. Use the “WireGaugeData” set to determine, via hypothesis testing at the = 0.05 level if there is a difference in wire diameter.
7. A courier service advertises that its average delivery time is less than 6 hours for local deliveries. A random sample of times for 12 deliveries to an address across town was recorded. These data are shown below. Is this sufficient evidence to support the courier’s advertisement at the 5% level of significance? Delivery time data: 3.03, 6.33, 6.50, 5.22, 3.56, 6.76, 7.98, 4.82, 7.96, 4.54, 5.09, 6.46
8. Mike’s Bikes in Columbus, Georgia sells a great many road bikes. One of the things that causes Mike Reynolds (the store’s proprietor) heartburn is customers coming back in with tire problems. If too much air is put into the tires, blowouts can occur, which are dangerous. In addition to blowouts, the inner tubes must be replaced, which is difficult. If too little air is put into the tires, poor bike performance results, specifically frequent tire replacement. Mike is wondering if his mechanics are putting the correct amount of air in the tires. The correct amount of air needed for the tires is 115 psi (pounds of air pressure per square inch). Mike randomly sampled 100 inflated tires, and discovered the mean tire pressure to be 113.58 psi, with a standard deviation of 8.1 psi. At the α = 0.08 level, what can we conclude about the tire pressure at Mike’s?
9. ThreeGuys Chemical Corporation in Cincinnati has a new sodium nitrate rust inhibitor out. The product (called The MoistureBasher) is marketed as a process additive for machine parts used in high-humidity environments. Three Guys claims that when using the MoistureBasher, machine parts can last for 90 days prior to needing replaced due to rusting. A consumer-advocacy group based in Boston decided to test this claim of ThreeGuys – they believe the rust protection is less than 90 days. They treated 20 machine parts with the MoistureBasher and measured the usable duration of machines parts treated with the product. They found a mean duration of 81 days with a standard deviation of 2.5 days. What does this sample information say about the performance claim of ThreeGuys?
10. Individuals filing Federal Income Tax returns prior to March 31 had an average refund of $1,056. Consider the population of “last minute” filers who mail their returns during the last five days of the income tax period (April 10-15). A sample of 400 late filers was collected, and it was determined that their average refund was $910 with a standard deviation of $1,600. Do late filers receive a refund less than $1,056? Use α = 0.05.
11. Ten years ago, the A.C. Nielson service claimed that on average, an American household watched 6.70 hours of television per day. An independent market research group believes that more television is watched now. To test this claim, 200 households were surveyed, and they found a mean of 7.25 hours of television are watched now, with a standard deviation of 2.5 hours. Has the amount of television viewing increased over the last ten years? Use α = 0.02.
12. Historically, evening long-distance phone calls from a particular city average 15.2 minutes per call. In a random sample of 35 calls, the sample mean time was 14.3 minutes per call, with a sample standard deviation of 5 minutes. Use this sample information to test for any change in the mean duration of long-distance phone calls. Use = 0.02.
13. A manufacturer of a nylon rope claims that their 10 mm rope withstands a load of more than 250 pounds of force before breaking. To validate this claim, several ropes were subjected to loads and the force at which they broke was documented. These forces are expressed in pounds, and are as follows: 280, 259, 255, 238, 245, 265, 250, 259, 241 and 260. Use α = 0.06. Is the manufactures claim credible?14. A large manufacturer of an electronic component claims that their 0.5 V connecter is consistently produced at a rate of less than 10 defective units per million units produced. Sampling has revealed that the last several lots had defects per million units produced as follows: 3, 8, 7, 13, 8, 4, 11, 10, 9, 6, 10 and 8. Is the manufacturer’s claim of less than 10 defects per million legitimate? Use α = 0.04.
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