1. In a survey of 1000 American adults conducted in April 2012, 43% reported having gone through an entire week without paying for anything in cash. Test to see if this sample provides evidence that the proportion of all American adults going a week without paying cash is greater than 40%. Use the fact that a randomization distribution is approximately normally distributed with a standard error of SE = 0.016. Show all details of the test and use a 5% significance level.(hypotheses, define the parameters, test statistic, p-value, justification for conclusion, conclusion about the null, and conclusion in context of the problem.)

2. Hospital admissions for asthma in children younger than 15 years was studied inScotland both before and after comprehensive smoke-free legislation was passed in March 2006. Monthly records were kept of the annualized percent change in asthma admissions. For the sample studied, before the legislation, admissions for asthma were increasing at a mean rate of 5.2% per year. The standard error for this estimate is 0.7% per year. After the legislation, admissions were decreasing at a mean rate of 18.2% per year, with a standard error of 1.79%. In both cases, the sample size is large enough to use a normal distribution. Note: the mean decrease of 18.2% means that we work with a value of -18.2%.

a) Find and interpret a 95% confidence interval for the mean annual percentage rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation.

b) Find a 95% confidence interval for the same quantity after legislation.

c) Is this an experiment or an observational study?

d) The evidence is quite compelling. Can we conclude cause and effect?