Introduction to Statistics Homework #5 Solutions STAT 200

. (3 points): Stephen Stigler determined in 1977 that the speed of light is 299,710.5 km/sec. In 1882, Albert Michelson had collected measurements on the speed of light ("Student t-distribution," 2013). Is there evidence to show that Michelson’s data is different from Stigler’s value of the speed of light? a.) State the random variable For this problem, the random variable will be: x = speed of light measured by Albert Michelson b.) State the population parameter The population parameter will be: μ = mean speed of light measured by Albert Michelson c.) State the hypotheses The hypotheses for this experiment are given by: H0: μ = 299, 710. 5 km/s HA: μ ≠ 299, 710. 5 km/s 2.(3 points): According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? a.) State the type I error in this case, consequences of this error type for this situation, and the appropriate alpha level to use. In this situation, the Type I error is saying that the proportion of complaints from identity theft in Alaska is less than 23%, when it is 23%. One consequence of this error is that the Federal Trade Commission (FTC) would think that identity theft isn’t as big as a problem when it is. Thus, the FTC may not put as much effort into stopping or investigating identity theft in Alaska as it should. b.) State the type II error in this case, consequences of this error type for this situation, and the appropriate alpha level to use. Type II error: saying that the proportion of complaints from identity theft in Alaska is 23%, when it is less than 23%. One consequence of this error is that the Federal Trade Commission would put more effort into Alaska then it needs to. Thus, resources that could be used other places will be wasted in Alaska. The best alpha level in this case would be 1%, since a type I error looks to have worse consequences than a type II error.