Please show your work and explain.

1.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 = 800 g. Calculate the 95% confidence interval for the mean birth weight of SIDS cases in the county. Interpret your results.

2.True or false? Given that a confidence interval for is 13 + 5.

a.The value of 13 in this expression is the point estimate.

b.The value 5 in this expression is the estimate's standard error.

c.The value 5 in this expression is the estimate's margin of error.

d.The width of the confidence interval is 5.

3.When do we use a t-statistic instead of a z-statistic to help infer a mean?

4.Identify whether the studies described here are based on (1) single samples, (2) paired samples, or (3) independent samples.

a.Cardiovascular disease risk factors are compared in husbands and wives.

b.A nutritional exam is applied to a random sample of individuals. Results are compared to the results of the whole nation.

c.An investigator compares vaccination histories in 30 autistic schoolchildren to a simple random sample of non-autistic children from the same school district.

5.Identify two graphical methods that can be used to compare quantitative (continuous) data between two independent groups.

6.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.

7.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?

8.True or False:When using data from the same sample, the 95% confidence interval for will always support the results from a 2-sided, 1 sample t-test.Explain your reasoning.