# An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs.

Question
Study design
An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs.

2020-11-02
Step 1
Two study design can be used for this scenario:
(i) Two-Sample Independent t-test:
This test is used because:
(a) It is very easy to interpret the output of independent samples.
(b) A small number of subjects for independent t-test samples are required.
(c) T-test enables us to compare the average values of the two data set samples and determine whether the sample subjects come from the same population.
(d) The test gives you all the information you need to know about the population.
Step 2
(ii) Two samples Paired t-test:
This test is used because:
(a) T-test repeated measure design results in small effects since the amount of error from samples is very small.
(b) Only one group is available for testing and this can result in less noise of data.
(c) Only one value from each subject is needed, it requires values of subjects from the two sample groups on a quantitative variable.
(d) Standard software programs that support statistical functions like Microsoft Excel can be used to calculate t-test data.

### Relevant Questions

1.An investigator wants to assess whether the use of a specific medication given to infants born prematurely is associated with developmental delay. Infants who were born prematurely are recruited and followed for 2-years.
Some of the infants were given the medication at birth and others were not. All infants will undergo extensive testing at age 2 to assess various aspects of development.
What type of study design: The Case Report/Case Series, The Cross-Sectional Survey, The Cohort Study, The Case Control Study, The Nested Case-Control Study, The Randomized Controlled Trial or The Crossover Trial?
In 2014, the Centers for Disearse reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of 0.30.
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b)Assume that the study uses your sample size recommendation in part (a) and finds 470 smokers. What is the point estimate of the proportion of smokers in the population? (Round your answer to four decimal places.)
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The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke $$\displaystyle{\left\langle{C}{D}{C}{w}{e}{b}{s}{i}{t}{e},{D}{e}{c}{e}{m}{b}{e}{r}{14},{2014}\right\rangle}$$. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30.
a.How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02(to the nearest whole number)? Use 95% confidence.
b.Assume that the study uses your sample size recommendation in part(a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population(to 4 decimals)?
c.What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?
The centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and Questions Navigation Menu preliminary estimate of the proportion who smoke of .26.
a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02?(to the nearest whole number) Use 95% confidence.
b) Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?
c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?
The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke to be .30.
a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 2%? Use 95% confidence.
b) Assume that the study uses your sample size recommendation above and finds 520 smokers. What is the point estimate of the proportion of smokers in the population?
c) What is the 95% confidence interval for the proportion of smokers in the population?
The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30.
a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02? Use 95% confidence.
c) Using an $$\displaystyle\alpha\le{v}{e}{l}{o}{f}{.05}{\left(\alpha={.05}\right)}$$, identify the critical values of t for a 2-tailed test.
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