STAT 200 Week 5 Homework Problems

STAT 200 Week 5 Homework Problems 7.1.4 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? State the random variable, population parameter, and hypotheses. Yes, Michelson’s data is different from Stigler’s value. Random variable: speed of light measured by Stigler Population parameter: speed of light measured by Michelson Null Hypothesis, H0: µ=.5 km/sec Alternative Hypothesis, HA: µ≠.5 km/sec 7.1.6 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%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use. Population proportion: P=0.23 # of samples: n=1432 Alaska complaints: x=321 Sample proportion: pˆ= x/n = 321/1432= 0.2242 H0: P=0.23 HA: P < 0.23