Question 2 There has been a long-standing need for a technique that can provide fast, accurate and precise results regarding the presence of hazardous levels of lead in settled house dust. Several home testing kits are now available. One kit manufactured by Hybrivet (LeadCheck Swabs) is advertised as able to detect lead dust levels that exceed the U.S. Environmental Protection Agency's dust lead standard for floors (40 ug/ft2). You would like to investigate Hybrivet's claims. You are interested in the proportion of test swabs that correctly detect high lead dust levels. a) You'd like to find a 99% confidence interval for the proportion of swabs that correctly detect high lead dust levels to within 3 percentage points. Your budget is $600. If it costs $5 per test strip to do the test, will you be able to take the needed sample? Show detailed calculations (calculate the minimum sample size first, based on this you make your decision) b) Due to the budgetary constraints given above, you take a random sample of 250 test swabs. It is reasonable here to assume the different swabs are independent. You find that 45 of the swabs test positive for high lead. Calculate a 99% confidence interval for the true proportion of positive test results.c)Does the true population proportion lie in the interval calculated above? Yes No Can not tell d) Answer the following for the 99% confidence interval, assuming all other values remain the same. Just circle the right answer. (i) How would the width of the confidence interval change if the confidence level decreases to 95%? Would the width Increase decrease or remain the same? (ii) How would the width of the confidence interval change if the sample size n is increased? Would the width Increase decrease or remain the same