Hospital admissions for asthma in children younger than 15 years was studied1 in Scotland 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, both before and after the legislation was passed. 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 for this mean of 1.79%. In both cases, the sample size is large enough to use a normal distribution. a) Find a 90% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation. b) Find a 90% confidence interval for the same quantity after the legislation

Question

Mathematics

Esmeralda Maynard

17 February, 17:02

Hospital admissions for asthma in children younger than 15 years was studied1 in Scotland 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, both before and after the legislation was passed. 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 for this mean of 1.79%. In both cases, the sample size is large enough to use a normal distribution. a) Find a 90% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation. b) Find a 90% confidence interval for the same quantity after the legislation

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April Friedman · Answer 1

(a) A 90% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation is between 4.5% and 5.9%

(b) A 90% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland after the smoke-free legislation is between 16.41% and 19.99%

Step-by-step explanation:

Confidence Interval = mean% + or - standard error%

Before the smoke-free legislation, CI=5.2%+0.7%=5.9%

CI=5.2%-0.7%=4.5%

CI is between 4.5% and 5.9%

After the smoke-free legislation

CI=18.2%+1.79%=19.99%

CI=18.2%-1.79%=16.41%

CI is between 16.41% and 19.99%