# Final quiz-4 | Mathematics homework help

Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 2.5 points.

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

2. A vaccine manufacturer analyzes a batch of product to check its titer. Immunologic analyses are imperfect, and repeated measurements on the same batch are expected to yield slightly different titers. Assume titer measurements vary according to a normal distribution with mean µ and σ = 0.070. Three measurements demonstrate titers of 7.40, 7.36 and 7.45. Calculate a 95% confidence interval for true concentration of the sample.

3. True or false? A confidence interval for µ is 13 + 5.

a. The value 5 in this expression is the estimate’s standard error.

b. The value 13 in this expression is the estimate’s margin of error.

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

4. The term *critical value* is often used to refer to the value of a test statistic that determines statistical significance at some fixed α level for a test. For example, +1.96 are the critical values for a two-tailed *z*-test at α = 0.05. In performing a *t*-test based on 21 observations, what are the critical values for a one-tailed test when α = 0.05? That is, what values of the *t*_{stat} will give a one-sided *p*-value that is less than or equal to 0.05? What are the critical values for a two-tailed test at α = 0.05?

5. When do you use a *t*-procedure instead of a *z*-procedure to help infer a mean?

6. A simple random sample of *n* = 26 boys between the ages of 13 and 14 has a mean height of 63.8 inches with a standard deviation 3.1 inches. Calculate a 95% confidence interval for the mean height of the population.

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

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

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

c. A nutritional exam in applied to a random sample of individuals. Results are compared to expected means and proportions.

8. We wish to detect a mean difference of 0.25 for a variable that has a standard deviation of 0.67. How large a sample is needed to detect the mean differences with 90% power at α = 0.05 (two-sided)?

9. Identify two graphical methods that can be used to compare quantitative data from two independent groups.

10. 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.