- 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.
The 95% CI for u= 2998 +/- (1.96) 800/sqr 49= 2998 +/- 224= (2774 to 3222)
There is 95% confidence that the population mean is between 2774 and 3222.
- True or false? Given that a confidence interval for µ is 13 + 5.
- The value of 13 in this expression is the point estimate.
True
- The value 5 in this expression is the estimate’s standard error.
False; 5 is margin of error
- The value 5 in this expression is the estimate’s margin of error.
True
- The width of the confidence interval is 5. False; width is 10
- When do we use a t-statistic instead of a z-statistic to help infer a mean?
When the standard error of the mean is uncertain, a t-statistic is used. Their broader tails accommodate the uncertainty that comes from estimating the σ and s.
- 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.
Paired samples
- A nutritional exam is applied to a random sample of individuals. Results are compared to the results of the whole nation.
Single sample
- An investigator compares vaccination histories in 30 autistic school children to a simple random sample of non-autistic children from the same school district.
Independent samples
- Identify two graphical methods that can be used to compare quantitative (continuous) data between two independent groups.
Back-to-back stemplots Side-by-side boxplots
- 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.
The boys have lower scores on average and less variability. There is one outlier in the girls group.
— When looking at the graphs the risk taking behavior is way lower in the boys than the girls. The boys have a great spread , but he girls spread is higher than the boys. The boys values are low sits at 75-125, where the girls value sit at 89-130. The median for boys is 95 and the girls median is a little higher sitting at 105.5. The interesting thing is the boys had one high outliner sitting at 126.
- 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? — If you really look at it from a statisical look the study that has 90% power would be the one sample that need the larger sample size because of the smaller power that is being used.
- 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. — This statement happens to be true , the confidence gives a lower and upper limit that really helps to establish all the parameters that falls within the normal range of 95%.
