1. Suppose that a life insurance company has sold a variety of one-year term policies, which together brought in $10,000,000 in revenue. Say that these policies pay an average of $100,000 in the event that someone dies. Say that they also sold 50,000 of these policies. What they are naturally concerned about is the possibility that more than 100 people out of this 50,000 die in a year, since they would have to pay out (as an estimate ) more than $100,000 =$10,000,000 resulting in a net loss. Estimate the probability that 100 or more people out of 50,000 will die in a particular year, given that the average death rate for this company's customers has historically been 1 in 2000. This is asking for an estimate of a probability that a binomial random variable has a certain value or greater.
2. According to the 2010 census, 16% of the people in the U.S. are of hispanic or latino origin. One county supervisor believes her county has a different proportion of hispanic people than the nation as a whole. She looks at some recent survey data, which was a random sample of 437 county residents, and found that 44 surveyed are of hispanic origin.
a) State an appropriate null hypothesis and alternative hypothesis for her to consider as the framework for a one-proportion z-test.
b) Calculate the test statistic ( which means the z-score of the observed proportion) and use this value to place the sample proportion with reasonable accuracy on a sketch of the normal curve that one could use to model the sampling distribution of the proportion that she is interested in investigating here.
c) Calculate the p-value of the observed sample proportion
D) State your conclusion regarding the null hypothesis, based on your answer in (c)
3. In 1879, Albert Michelson measured the speed of light in an experiment that involved 100 different measurements. His average across this sample size of 100 was 299,852.4 km/sec and its standard deviation was s=79. Modern scientists peg the speed of light at 299,710.5 km/sec. Lets investigate the likelihood of getting michelson's results or something more extreme under the null assumption of today's estimated speed. To that end:
a) find the p-value for michelson's sample mean using a two-sided-alternative t-test
b) interpret the p-value- does it say that his result was likely or unlikely under the null hypothesis? What might that mean about the true speed of light? What might that mean about his experiment?