Quiz (Confidence Interval. Standard Error. t-statistic. z-statistic.)

A sample of 49 sudden infant death syndrome (SIDS) cases had a mean birth weight of 2998 g. Based on other births in the county, we will assume σ = 800 g. Calculate the 95% confidence interval for the mean birth weight of SIDS cases in the county. Interpret your results.
True or false? Given that a confidence interval for µ is 13 +

When do we use a t-statistic instead of a z-statistic to help infer a mean?
Identify whether the studies described here are based on (1) single samples, (2) paired samples, or (3) independent samples.

Cardiovascular disease risk factors are compared in husbands and wives
A nutritional exam is applied to a random sample of individuals. Results are compared to the results of the whole nation.
An investigator compares vaccination histories in 30 autistic schoolchildren to a simple random sample of non-autistic children from the same school district.

Identify two graphical methods that can be used to compare quantitative (continuous) data between two independent groups.
A questionnaire measures an index of risk-taking behavior in respondents. Scores are standardized so that 100 represents the population average. The questionnaire is applied to a sample of teenage boys and girls. The data for boys is {72, 73, 86, 95, 95, 95, 96, 97, 99, 125}. The data for girls is {89, 92, 93, 98, 105, 106, 110, 126, 127, 130}. Explore the group differences with side-by-side boxplots. Create the boxplots and then describe how risk taking behavior varies between genders.
Which study will require a larger sample size, one done with 80% power or 90% power when alpha (type I error) is set at 0.05 and we use the same population and expected difference and variation for both studies?
True or False: When using data from the same sample, the 95% confidence interval for µ will always support the results from a 2-sided, 1 sample t-test. Explain your reasoning.